2835:
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5355:
36:
5393:
5381:
773:
362:
514:
242:
1735:
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949:
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and boundedly complete, is necessarily minimal sufficient. Another form of
Bahadur's theorem states that any sufficient and boundedly complete statistic over a finite-dimensional coordinate space is also minimal sufficient.
152:. While an ancillary statistic contains no information about the model parameters, a complete statistic contains only information about the parameters, and no ancillary information. It is closely related to the concept of a
1822:
2345:
2106:
1055:
1616:
1493:
478:
1361:
2159:
1913:
1182:
768:{\displaystyle \operatorname {E} _{p}(g(T))=\sum _{t=0}^{n}{g(t){n \choose t}p^{t}(1-p)^{n-t}}=(1-p)^{n}\sum _{t=0}^{n}{g(t){n \choose t}\left({\frac {p}{1-p}}\right)^{t}}.}
835:
1997:
2040:
2217:
2182:
357:{\displaystyle {\text{if }}\operatorname {E} _{\theta }(g(T))=0{\text{ for all }}\theta {\text{ then }}\mathbf {P} _{\theta }(g(T)=0)=1{\text{ for all }}\theta .}
1541:
1395:
2588:
1631:
2350:
843:
2957:
2476:
If there is a minimal sufficient statistic then any complete sufficient statistic is also minimal sufficient. But there are pathological cases where a
2523:
loss function; in many practical applications with the squared loss-function, it has a smaller mean squared error among any estimators with the same
1746:
2253:
4490:
4995:
2754:"An Example of an Improvable RaoâBlackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator"
2680:"An Example of an Improvable RaoâBlackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator"
5145:
4769:
3410:
2488:
The notion of completeness has many applications in statistics, particularly in the following two theorems of mathematical statistics.
53:
2052:
100:
72:
4543:
4982:
79:
972:
2967:
2935:
2905:
2626:
1549:
3405:
3105:
1403:
4009:
3157:
2542:
86:
2736:
427:
17:
1283:
4792:
4684:
2878:
2856:
119:
2849:
68:
5397:
4970:
4844:
2111:
2981:
5028:
4689:
4434:
3805:
3395:
2641:
Young, G. A. and Smith, R. L. (2005). Essentials of
Statistical Inference. (p. 94). Cambridge University Press.
1841:
5079:
4291:
4098:
3987:
3945:
1099:
It is important to notice that the result that all coefficients must be 0 was obtained because of the range of
57:
4019:
2500:
5322:
4281:
3184:
2661:
4873:
4822:
4807:
4797:
4666:
4538:
4505:
4331:
4286:
4116:
2810:
5419:
5385:
5217:
5018:
4942:
4243:
3997:
3666:
3130:
5102:
5074:
5069:
4817:
4576:
4482:
4462:
4370:
4081:
3899:
3382:
3254:
2898:
Statistical information and likelihood : A collection of critical essays by Dr. D. Basu
1133:
4834:
4602:
4323:
4248:
4177:
4106:
4026:
4014:
3872:
3865:
3573:
3294:
93:
2930:(Second (updated printing 2007) of the Holden-Day 1976 ed.). Pearson Prentice–Hall.
5317:
5084:
4947:
4632:
4597:
4561:
4346:
3788:
3697:
3656:
3568:
3259:
3098:
2843:
2569:
2508:
2347:
is a minimal sufficient statistic and is a function of any other minimal sufficient statistic, but
1266:
789:
5226:
4839:
4779:
4716:
4354:
4338:
4076:
3938:
3928:
3778:
3692:
46:
5264:
5194:
4987:
4924:
4679:
4566:
3563:
3460:
3367:
3246:
3145:
2860:
1956:
413:
2002:
5289:
5231:
5174:
5000:
4893:
4802:
4528:
4412:
4271:
4263:
4153:
4145:
3960:
3856:
3834:
3793:
3758:
3725:
3671:
3646:
3601:
3540:
3500:
3302:
3125:
2187:
489:
5212:
4787:
4736:
4712:
4674:
4592:
4571:
4523:
4402:
4380:
4349:
4258:
4135:
4086:
4004:
3977:
3933:
3889:
3651:
3427:
3307:
3076:
3029:
2977:
2945:
2915:
2565:
2228:
153:
2650:
Casella, G. and Berger, R. L. (2001). Statistical
Inference. (pp. 285â286). Duxbury Press.
2164:
1103:. Had the parameter space been finite and with a number of elements less than or equal to
8:
5359:
5284:
5207:
4888:
4652:
4645:
4607:
4515:
4495:
4467:
4200:
4066:
4061:
4051:
4043:
3861:
3822:
3712:
3702:
3611:
3390:
3346:
3264:
3189:
3091:
2573:
1270:
1234:
1123:= 1 and the parameter space is {0.5}, a single observation and a single parameter value,
201:
149:
145:
1999:
is sufficient but not complete. It admits a non-zero unbiased estimator of zero, namely
1730:{\displaystyle \int _{-\infty }^{\infty }g(x)\exp \left(-(x-2\theta )^{2}/4\right)\,dx.}
5373:
5184:
5038:
4934:
4883:
4759:
4656:
4640:
4617:
4394:
4128:
4111:
4071:
3982:
3877:
3839:
3810:
3770:
3730:
3676:
3593:
3279:
3274:
3064:
3017:
2962:. Springer Texts in Statistics (Third ed.). New York: Springer. pp. xiv+784.
2778:
2753:
2704:
2679:
2592:
2477:
1526:
1380:
2800:
Casella, G. and Berger, R. L. (2001). Statistical
Inference. (pp. 287). Duxbury Press.
1942:) is zero almost everywhere. The exponential is not zero, so this can only happen if
156:
which contains all of the information that the dataset provides about the parameters.
5368:
5279:
5249:
5241:
5061:
5052:
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4908:
4764:
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4612:
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4419:
4407:
4033:
3950:
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3817:
3661:
3583:
3362:
3236:
2998:
2963:
2953:
2931:
2901:
2783:
2732:
2709:
2622:
2557:
1923:
148:
in relation to a parametric model of the dataset. It is opposed to the concept of an
2462:{\displaystyle 2\left(\sum _{i=1}^{n}X_{i}\right)^{2}-(n+1)\sum _{i=1}^{n}X_{i}^{2}}
944:{\displaystyle \sum _{t=0}^{n}g(t){n \choose t}\left({\frac {p}{1-p}}\right)^{t}=0.}
5304:
5259:
5023:
5010:
4903:
4878:
4812:
4744:
4622:
4230:
4123:
4056:
3969:
3916:
3735:
3606:
3400:
3284:
3199:
3166:
3054:
3007:
2773:
2765:
2699:
2691:
172:
3038:
2990:
2769:
2695:
5221:
4965:
4827:
4754:
4429:
4303:
4276:
4253:
4222:
3849:
3844:
3798:
3528:
3179:
3072:
3059:
3042:
3025:
3012:
2994:
2973:
2941:
2923:
2911:
2520:
1377:
To show this, it is sufficient to demonstrate that there is no non-zero function
165:
4711:
5170:
5165:
3628:
3558:
3204:
2524:
1084:
and, therefore, can only be identical to 0 if all coefficients are 0, that is,
1065:
5413:
5327:
5294:
5157:
5118:
4929:
4898:
4362:
4316:
3921:
3623:
3450:
3214:
3209:
396:
1817:{\displaystyle k(\theta )\int _{-\infty }^{\infty }h(x)e^{x\theta }\,dx\,\!}
5269:
5202:
5179:
5094:
4424:
3720:
3618:
3553:
3495:
3480:
3417:
3372:
2787:
2713:
2340:{\displaystyle \left(\sum _{i=1}^{n}X_{i},\sum _{i=1}^{n}X_{i}^{2}\right)}
5312:
5274:
4957:
4858:
4720:
4533:
4500:
3992:
3909:
3904:
3548:
3505:
3485:
3465:
3455:
3224:
3068:
3021:
4158:
3638:
3338:
3269:
3219:
3194:
3114:
2596:
1077:
133:
4311:
4163:
3783:
3578:
3490:
3475:
3470:
3435:
2893:
2534:
then several alternative statistics exist for unbiased estimation of
2519:. In other words, this statistic has a smaller expected loss for any
197:
141:
35:
3827:
3445:
3322:
3317:
3312:
1505:
That fact may be seen as follows. The probability distribution of
5332:
5033:
2928:
Mathematical statistics, Volume 1: Basic and selected topics
2101:{\textstyle X\sim \operatorname {Uniform} (\theta -1,\theta +1).}
2231:
does not exist (for example, see Galili and
Meilijson 2016 ).
5254:
4235:
4209:
4189:
3440:
3231:
2530:
Examples exists that when the minimal sufficient statistic is
2044:
3083:
3043:"Completeness, similar regions, and unbiased estimation. II"
2995:"Completeness, similar regions, and unbiased estimation. I."
2480:
statistic does not exist even if a complete statistic does.
3174:
2751:
2677:
1107:, it might be possible to solve the linear equations in
1050:{\displaystyle \sum _{t=0}^{n}g(t){n \choose t}r^{t}=0.}
379:
if this implication holds for every measurable function
2900:. Lecture Notes in Statistics. Vol. 45. Springer.
2515:, then it is the best mean-unbiased estimator for
2538:, while some of them have lower variance than others.
2190:
2167:
2114:
2055:
2005:
1959:
1611:{\displaystyle \exp \left(-(x-2\theta )^{2}/4\right).}
431:
2503:, which states that if a statistic that is unbiased,
2353:
2256:
1844:
1749:
1634:
1552:
1529:
1523:
and variance 2. Its probability density function in
1406:
1383:
1286:
1136:
975:
846:
792:
517:
430:
391:
The
Bernoulli model admits a complete statistic. Let
245:
4996:
Autoregressive conditional heteroskedasticity (ARCH)
2222:
1488:{\displaystyle g(s(X_{1},X_{2}))=g(X_{1}+X_{2})\,\!}
1127:
is not complete. Observe that, with the definition:
1119:
and get solutions different from 0. For example, if
60:. Unsourced material may be challenged and removed.
4458:
2461:
2339:
2211:
2176:
2153:
2100:
2034:
1991:
1907:
1816:
1729:
1610:
1535:
1487:
1389:
1355:
1176:
1049:
943:
829:
767:
472:
356:
1904:
1813:
1484:
1352:
1025:
1012:
896:
883:
722:
709:
602:
589:
473:{\displaystyle \textstyle T=\sum _{i=1}^{n}X_{i}}
424:be the number of 1s observed in the sample, i.e.
5411:
1356:{\displaystyle s((X_{1},X_{2}))=X_{1}+X_{2}\,\!}
508:is a complete statistic. To see this, note that
4544:Multivariate adaptive regression splines (MARS)
3036:
2988:
2591:. In the case where there exists at least one
2154:{\textstyle \operatorname {E} (\sin(\pi X))=0}
3099:
2726:
2616:
2560:, which states that a statistic that is both
2483:
2473:, so there cannot be a complete statistic.
2922:
1269:, identically distributed random variables,
171:whose probability distribution belongs to a
2952:
2752:Tal Galili; Isaac Meilijson (31 Mar 2016).
2678:Tal Galili; Isaac Meilijson (31 Mar 2016).
2045:Example: Location of a uniform distribution
386:
3144:
3106:
3092:
2727:Casella, George; Berger, Roger L. (2001).
2617:Casella, George; Berger, Roger W. (2001).
2491:
1908:{\displaystyle h(x)=g(x)e^{-x^{2}/4}.\,\!}
1625:above would therefore be a constant times
1214:
3757:
3058:
3047:SankhyÄ: The Indian Journal of Statistics
3011:
2999:SankhyÄ: the Indian Journal of Statistics
2879:Learn how and when to remove this message
2777:
2703:
2227:For some parametric families, a complete
1934:), and cannot be identically zero unless
1903:
1812:
1805:
1717:
1483:
1351:
1219:This example will show that, in a sample
1173:
1115:) obtained by substituting the values of
120:Learn how and when to remove this message
2842:This article includes a list of general
2234:For example, if you take a sample sized
1498:remains zero regardless of the value of
14:
5412:
5070:KaplanâMeier estimator (product limit)
5143:
4710:
4457:
3756:
3526:
3143:
3087:
2811:"Statistical Inference Lecture Notes"
2720:
1251:is complete and sufficient. Suppose (
5380:
5080:Accelerated failure time (AFT) model
2892:
2828:
2579:
58:adding citations to reliable sources
29:
5392:
4675:Analysis of variance (ANOVA, anova)
3527:
2543:minimum-variance unbiased estimator
1237:with known variance, the statistic
24:
4770:CochranâMantelâHaenszel statistics
3396:Pearson product-moment correlation
2848:it lacks sufficient corresponding
2659:
2115:
1775:
1770:
1648:
1643:
1016:
887:
713:
593:
519:
252:
233:if, for every measurable function
25:
5431:
2662:"Uniqueness of Laplace Transform"
2548:
2223:Relation to sufficient statistics
1740:A bit of algebra reduces this to
1060:First, observe that the range of
5391:
5379:
5367:
5354:
5353:
5144:
2833:
2595:statistic, a statistic which is
2469:has an expectation of 0 for all
1177:{\displaystyle g(t)=2(t-0.5),\,}
303:
200:; that is, the composition of a
34:
5029:Least-squares spectral analysis
2731:(2nd ed.). Duxbury Press.
45:needs additional citations for
4010:Mean-unbiased minimum-variance
3113:
2959:Testing statistical hypotheses
2803:
2794:
2745:
2671:
2653:
2644:
2635:
2610:
2420:
2408:
2206:
2197:
2142:
2139:
2130:
2121:
2092:
2068:
1986:
1960:
1869:
1863:
1854:
1848:
1789:
1783:
1759:
1753:
1695:
1679:
1662:
1656:
1583:
1567:
1480:
1454:
1445:
1442:
1416:
1410:
1322:
1319:
1293:
1290:
1167:
1155:
1146:
1140:
1006:
1000:
877:
871:
818:
815:
809:
803:
703:
697:
663:
650:
631:
618:
583:
577:
546:
543:
537:
531:
500:). If the parameter space for
334:
325:
319:
313:
279:
276:
270:
264:
69:"Completeness" statistics
13:
1:
5323:Geographic information system
4539:Simultaneous equations models
2824:
2770:10.1080/00031305.2015.1100683
2696:10.1080/00031305.2015.1100683
1950:) is zero almost everywhere.
1543:is therefore proportional to
1397:such that the expectation of
1092:) = 0 for all
830:{\displaystyle E_{p}(g(T))=0}
159:
4506:Coefficient of determination
4117:Uniformly most powerful test
3060:10.1007/978-1-4614-1412-4_24
3013:10.1007/978-1-4614-1412-4_23
2956:; Romano, Joseph P. (2005).
1519:is normal with expectation 2
7:
5075:Proportional hazards models
5019:Spectral density estimation
5001:Vector autoregression (VAR)
4435:Maximum posterior estimator
3667:Randomized controlled trial
2926:; Doksum, Kjell A. (2001).
2896:(1988). J. K. Ghosh (ed.).
2161:regardless of the value of
1953:By contrast, the statistic
10:
5436:
4835:Multivariate distributions
3255:Average absolute deviation
2484:Importance of completeness
1992:{\textstyle (X_{1},X_{2})}
778:Observe also that neither
5349:
5303:
5240:
5193:
5156:
5152:
5139:
5111:
5093:
5060:
5051:
5009:
4956:
4917:
4866:
4857:
4823:Structural equation model
4778:
4735:
4731:
4706:
4665:
4631:
4585:
4552:
4514:
4481:
4477:
4453:
4393:
4302:
4221:
4185:
4176:
4159:Score/Lagrange multiplier
4144:
4097:
4042:
3968:
3959:
3769:
3765:
3752:
3711:
3685:
3637:
3592:
3574:Sample size determination
3539:
3535:
3522:
3426:
3381:
3355:
3337:
3293:
3245:
3165:
3156:
3152:
3139:
3121:
2758:The American Statistician
2684:The American Statistician
2238: > 2 from a
2035:{\textstyle X_{1}-X_{2}.}
5318:Environmental statistics
4840:Elliptical distributions
4633:Generalized linear model
4562:Simple linear regression
4332:HodgesâLehmann estimator
3789:Probability distribution
3698:Stochastic approximation
3260:Coefficient of variation
2603:
2212:{\textstyle \sin(\pi X)}
1277:and variance 1. The sum
782:nor 1 −
387:Example: Bernoulli model
375:for the distribution of
229:for the distribution of
4978:Cross-correlation (XCF)
4586:Non-standard predictors
4020:LehmannâScheffĂŠ theorem
3693:Adaptive clinical trial
2863:more precise citations.
2501:LehmannâScheffĂŠ theorem
2492:LehmannâScheffĂŠ theorem
1215:Example: Sum of normals
5374:Mathematics portal
5195:Engineering statistics
5103:NelsonâAalen estimator
4680:Analysis of covariance
4567:Ordinary least squares
4491:Pearson product-moment
3895:Statistical functional
3806:Empirical distribution
3639:Controlled experiments
3368:Frequency distribution
3146:Descriptive statistics
2463:
2443:
2383:
2341:
2316:
2282:
2213:
2178:
2155:
2102:
2036:
1993:
1909:
1835:) is nowhere zero and
1818:
1731:
1612:
1537:
1489:
1391:
1357:
1178:
1051:
996:
958:/(1 −
945:
867:
831:
769:
692:
572:
474:
458:
414:Bernoulli distribution
383:that is also bounded.
358:
5290:Population statistics
5232:System identification
4966:Autocorrelation (ACF)
4894:Exponential smoothing
4808:Discriminant analysis
4803:Canonical correlation
4667:Partition of variance
4529:Regression validation
4373:(JonckheereâTerpstra)
4272:Likelihood-ratio test
3961:Frequentist inference
3873:Locationâscale family
3794:Sampling distribution
3759:Statistical inference
3726:Cross-sectional study
3713:Observational studies
3672:Randomized experiment
3501:Stem-and-leaf display
3303:Central limit theorem
2729:Statistical Inference
2619:Statistical inference
2464:
2423:
2363:
2342:
2296:
2262:
2250:) distribution, then
2214:
2179:
2177:{\textstyle \theta .}
2156:
2103:
2037:
1994:
1910:
1819:
1732:
1613:
1538:
1490:
1392:
1358:
1179:
1052:
976:
946:
847:
832:
770:
672:
552:
490:binomial distribution
475:
438:
359:
204:with a random sample
185:parametrized by
5213:Probabilistic design
4798:Principal components
4641:Exponential families
4593:Nonlinear regression
4572:General linear model
4534:Mixed effects models
4524:Errors and residuals
4501:Confounding variable
4403:Bayesian probability
4381:Van der Waerden test
4371:Ordered alternative
4136:Multiple comparisons
4015:RaoâBlackwellization
3978:Estimating equations
3934:Statistical distance
3652:Factorial experiment
3185:Arithmetic-Geometric
2585:Bounded completeness
2554:Bounded completeness
2351:
2254:
2229:sufficient statistic
2188:
2165:
2112:
2053:
2003:
1957:
1922:this is a two-sided
1842:
1747:
1632:
1550:
1527:
1404:
1381:
1284:
1271:normally distributed
1134:
973:
844:
790:
515:
428:
243:
154:sufficient statistic
54:improve this article
5285:Official statistics
5208:Methods engineering
4889:Seasonal adjustment
4657:Poisson regressions
4577:Bayesian regression
4516:Regression analysis
4496:Partial correlation
4468:Regression analysis
4067:Prediction interval
4062:Likelihood interval
4052:Confidence interval
4044:Interval estimation
4005:Unbiased estimators
3823:Model specification
3703:Up-and-down designs
3391:Partial correlation
3347:Index of dispersion
3265:Interquartile range
2574:ancillary statistic
2511:for some parameter
2458:
2331:
1779:
1652:
1621:The expectation of
1235:normal distribution
345: for all
290: for all
202:measurable function
150:ancillary statistic
140:is a property of a
5420:Statistical theory
5305:Spatial statistics
5185:Medical statistics
5085:First hitting time
5039:Whittle likelihood
4690:Degrees of freedom
4685:Multivariate ANOVA
4618:Heteroscedasticity
4430:Bayesian estimator
4395:Bayesian inference
4244:KolmogorovâSmirnov
4129:Randomization test
4099:Testing hypotheses
4072:Tolerance interval
3983:Maximum likelihood
3878:Exponential family
3811:Density estimation
3771:Statistical theory
3731:Natural experiment
3677:Scientific control
3594:Survey methodology
3280:Standard deviation
2593:minimal sufficient
2562:boundedly complete
2478:minimal sufficient
2459:
2444:
2337:
2317:
2209:
2174:
2151:
2098:
2032:
1989:
1905:
1814:
1762:
1727:
1635:
1608:
1533:
1485:
1387:
1368:complete statistic
1353:
1174:
1047:
941:
827:
765:
484:is a statistic of
470:
469:
373:boundedly complete
354:
18:Complete statistic
5407:
5406:
5345:
5344:
5341:
5340:
5280:National accounts
5250:Actuarial science
5242:Social statistics
5135:
5134:
5131:
5130:
5127:
5126:
5062:Survival function
5047:
5046:
4909:Granger causality
4750:Contingency table
4725:Survival analysis
4702:
4701:
4698:
4697:
4554:Linear regression
4449:
4448:
4445:
4444:
4420:Credible interval
4389:
4388:
4172:
4171:
3988:Method of moments
3857:Parametric family
3818:Statistical model
3748:
3747:
3744:
3743:
3662:Random assignment
3584:Statistical power
3518:
3517:
3514:
3513:
3363:Contingency table
3333:
3332:
3200:Generalized/power
2969:978-0-387-98864-1
2937:978-0-13-850363-5
2907:978-0-387-96751-6
2889:
2888:
2881:
2628:978-1-032-59303-6
2589:Bahadur's theorem
2580:Bahadur's theorem
2219:is not complete.
1924:Laplace transform
1918:As a function of
1536:{\displaystyle x}
1390:{\displaystyle g}
1273:with expectation
1233:of size 2 from a
1023:
923:
894:
749:
720:
600:
492:with parameters (
346:
299:
291:
249:
130:
129:
122:
104:
16:(Redirected from
5427:
5395:
5394:
5383:
5382:
5372:
5371:
5357:
5356:
5260:Crime statistics
5154:
5153:
5141:
5140:
5058:
5057:
5024:Fourier analysis
5011:Frequency domain
4991:
4938:
4904:Structural break
4864:
4863:
4813:Cluster analysis
4760:Log-linear model
4733:
4732:
4708:
4707:
4649:
4623:Homoscedasticity
4479:
4478:
4455:
4454:
4374:
4366:
4358:
4357:(KruskalâWallis)
4342:
4327:
4282:Cross validation
4267:
4249:AndersonâDarling
4196:
4183:
4182:
4154:Likelihood-ratio
4146:Parametric tests
4124:Permutation test
4107:1- & 2-tails
3998:Minimum distance
3970:Point estimation
3966:
3965:
3917:Optimal decision
3868:
3767:
3766:
3754:
3753:
3736:Quasi-experiment
3686:Adaptive designs
3537:
3536:
3524:
3523:
3401:Rank correlation
3163:
3162:
3154:
3153:
3141:
3140:
3108:
3101:
3094:
3085:
3084:
3080:
3062:
3033:
3015:
2985:
2980:. Archived from
2949:
2924:Bickel, Peter J.
2919:
2884:
2877:
2873:
2870:
2864:
2859:this article by
2850:inline citations
2837:
2836:
2829:
2818:
2817:
2815:
2807:
2801:
2798:
2792:
2791:
2781:
2749:
2743:
2742:
2724:
2718:
2717:
2707:
2675:
2669:
2668:
2666:
2660:Orloff, Jeremy.
2657:
2651:
2648:
2642:
2639:
2633:
2632:
2614:
2468:
2466:
2465:
2460:
2457:
2452:
2442:
2437:
2404:
2403:
2398:
2394:
2393:
2392:
2382:
2377:
2346:
2344:
2343:
2338:
2336:
2332:
2330:
2325:
2315:
2310:
2292:
2291:
2281:
2276:
2218:
2216:
2215:
2210:
2183:
2181:
2180:
2175:
2160:
2158:
2157:
2152:
2107:
2105:
2104:
2099:
2041:
2039:
2038:
2033:
2028:
2027:
2015:
2014:
1998:
1996:
1995:
1990:
1985:
1984:
1972:
1971:
1914:
1912:
1911:
1906:
1899:
1898:
1894:
1889:
1888:
1823:
1821:
1820:
1815:
1804:
1803:
1778:
1773:
1736:
1734:
1733:
1728:
1716:
1712:
1708:
1703:
1702:
1651:
1646:
1617:
1615:
1614:
1609:
1604:
1600:
1596:
1591:
1590:
1542:
1540:
1539:
1534:
1494:
1492:
1491:
1486:
1479:
1478:
1466:
1465:
1441:
1440:
1428:
1427:
1396:
1394:
1393:
1388:
1362:
1360:
1359:
1354:
1350:
1349:
1337:
1336:
1318:
1317:
1305:
1304:
1195:)) = 0 although
1183:
1181:
1180:
1175:
1056:
1054:
1053:
1048:
1040:
1039:
1030:
1029:
1028:
1015:
995:
990:
950:
948:
947:
942:
934:
933:
928:
924:
922:
908:
901:
900:
899:
886:
866:
861:
837:if and only if:
836:
834:
833:
828:
802:
801:
786:can be 0. Hence
774:
772:
771:
766:
761:
760:
759:
754:
750:
748:
734:
727:
726:
725:
712:
691:
686:
671:
670:
646:
645:
644:
617:
616:
607:
606:
605:
592:
571:
566:
527:
526:
479:
477:
476:
471:
468:
467:
457:
452:
363:
361:
360:
355:
347:
344:
312:
311:
306:
300:
298: then
297:
292:
289:
260:
259:
250:
247:
173:parametric model
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
5435:
5434:
5430:
5429:
5428:
5426:
5425:
5424:
5410:
5409:
5408:
5403:
5366:
5337:
5299:
5236:
5222:quality control
5189:
5171:Clinical trials
5148:
5123:
5107:
5095:Hazard function
5089:
5043:
5005:
4989:
4952:
4948:BreuschâGodfrey
4936:
4913:
4853:
4828:Factor analysis
4774:
4755:Graphical model
4727:
4694:
4661:
4647:
4627:
4581:
4548:
4510:
4473:
4472:
4441:
4385:
4372:
4364:
4356:
4340:
4325:
4304:Rank statistics
4298:
4277:Model selection
4265:
4223:Goodness of fit
4217:
4194:
4168:
4140:
4093:
4038:
4027:Median unbiased
3955:
3866:
3799:Order statistic
3761:
3740:
3707:
3681:
3633:
3588:
3531:
3529:Data collection
3510:
3422:
3377:
3351:
3329:
3289:
3241:
3158:Continuous data
3148:
3135:
3117:
3112:
3037:Lehmann, E.L.;
2989:Lehmann, E.L.;
2970:
2938:
2908:
2885:
2874:
2868:
2865:
2855:Please help to
2854:
2838:
2834:
2827:
2822:
2821:
2816:. July 7, 2022.
2813:
2809:
2808:
2804:
2799:
2795:
2750:
2746:
2739:
2725:
2721:
2676:
2672:
2664:
2658:
2654:
2649:
2645:
2640:
2636:
2629:
2615:
2611:
2606:
2587:also occurs in
2582:
2551:
2494:
2486:
2453:
2448:
2438:
2427:
2399:
2388:
2384:
2378:
2367:
2362:
2358:
2357:
2352:
2349:
2348:
2326:
2321:
2311:
2300:
2287:
2283:
2277:
2266:
2261:
2257:
2255:
2252:
2251:
2225:
2189:
2186:
2185:
2166:
2163:
2162:
2113:
2110:
2109:
2054:
2051:
2050:
2047:
2023:
2019:
2010:
2006:
2004:
2001:
2000:
1980:
1976:
1967:
1963:
1958:
1955:
1954:
1890:
1884:
1880:
1876:
1872:
1843:
1840:
1839:
1796:
1792:
1774:
1766:
1748:
1745:
1744:
1704:
1698:
1694:
1675:
1671:
1647:
1639:
1633:
1630:
1629:
1592:
1586:
1582:
1563:
1559:
1551:
1548:
1547:
1528:
1525:
1524:
1518:
1511:
1474:
1470:
1461:
1457:
1436:
1432:
1423:
1419:
1405:
1402:
1401:
1382:
1379:
1378:
1345:
1341:
1332:
1328:
1313:
1309:
1300:
1296:
1285:
1282:
1281:
1264:
1257:
1250:
1243:
1232:
1225:
1217:
1203:) is not 0 for
1135:
1132:
1131:
1035:
1031:
1024:
1011:
1010:
1009:
991:
980:
974:
971:
970:
929:
912:
907:
903:
902:
895:
882:
881:
880:
862:
851:
845:
842:
841:
797:
793:
791:
788:
787:
755:
738:
733:
729:
728:
721:
708:
707:
706:
693:
687:
676:
666:
662:
634:
630:
612:
608:
601:
588:
587:
586:
573:
567:
556:
522:
518:
516:
513:
512:
504:is (0,1), then
463:
459:
453:
442:
429:
426:
425:
416:with parameter
411:
403:such that each
389:
343:
307:
302:
301:
296:
288:
255:
251:
246:
244:
241:
240:
217:
210:
184:
166:random variable
162:
126:
115:
109:
106:
63:
61:
51:
39:
28:
27:Statistics term
23:
22:
15:
12:
11:
5:
5433:
5423:
5422:
5405:
5404:
5402:
5401:
5389:
5377:
5363:
5350:
5347:
5346:
5343:
5342:
5339:
5338:
5336:
5335:
5330:
5325:
5320:
5315:
5309:
5307:
5301:
5300:
5298:
5297:
5292:
5287:
5282:
5277:
5272:
5267:
5262:
5257:
5252:
5246:
5244:
5238:
5237:
5235:
5234:
5229:
5224:
5215:
5210:
5205:
5199:
5197:
5191:
5190:
5188:
5187:
5182:
5177:
5168:
5166:Bioinformatics
5162:
5160:
5150:
5149:
5137:
5136:
5133:
5132:
5129:
5128:
5125:
5124:
5122:
5121:
5115:
5113:
5109:
5108:
5106:
5105:
5099:
5097:
5091:
5090:
5088:
5087:
5082:
5077:
5072:
5066:
5064:
5055:
5049:
5048:
5045:
5044:
5042:
5041:
5036:
5031:
5026:
5021:
5015:
5013:
5007:
5006:
5004:
5003:
4998:
4993:
4985:
4980:
4975:
4974:
4973:
4971:partial (PACF)
4962:
4960:
4954:
4953:
4951:
4950:
4945:
4940:
4932:
4927:
4921:
4919:
4918:Specific tests
4915:
4914:
4912:
4911:
4906:
4901:
4896:
4891:
4886:
4881:
4876:
4870:
4868:
4861:
4855:
4854:
4852:
4851:
4850:
4849:
4848:
4847:
4832:
4831:
4830:
4820:
4818:Classification
4815:
4810:
4805:
4800:
4795:
4790:
4784:
4782:
4776:
4775:
4773:
4772:
4767:
4765:McNemar's test
4762:
4757:
4752:
4747:
4741:
4739:
4729:
4728:
4704:
4703:
4700:
4699:
4696:
4695:
4693:
4692:
4687:
4682:
4677:
4671:
4669:
4663:
4662:
4660:
4659:
4643:
4637:
4635:
4629:
4628:
4626:
4625:
4620:
4615:
4610:
4605:
4603:Semiparametric
4600:
4595:
4589:
4587:
4583:
4582:
4580:
4579:
4574:
4569:
4564:
4558:
4556:
4550:
4549:
4547:
4546:
4541:
4536:
4531:
4526:
4520:
4518:
4512:
4511:
4509:
4508:
4503:
4498:
4493:
4487:
4485:
4475:
4474:
4471:
4470:
4465:
4459:
4451:
4450:
4447:
4446:
4443:
4442:
4440:
4439:
4438:
4437:
4427:
4422:
4417:
4416:
4415:
4410:
4399:
4397:
4391:
4390:
4387:
4386:
4384:
4383:
4378:
4377:
4376:
4368:
4360:
4344:
4341:(MannâWhitney)
4336:
4335:
4334:
4321:
4320:
4319:
4308:
4306:
4300:
4299:
4297:
4296:
4295:
4294:
4289:
4284:
4274:
4269:
4266:(ShapiroâWilk)
4261:
4256:
4251:
4246:
4241:
4233:
4227:
4225:
4219:
4218:
4216:
4215:
4207:
4198:
4186:
4180:
4178:Specific tests
4174:
4173:
4170:
4169:
4167:
4166:
4161:
4156:
4150:
4148:
4142:
4141:
4139:
4138:
4133:
4132:
4131:
4121:
4120:
4119:
4109:
4103:
4101:
4095:
4094:
4092:
4091:
4090:
4089:
4084:
4074:
4069:
4064:
4059:
4054:
4048:
4046:
4040:
4039:
4037:
4036:
4031:
4030:
4029:
4024:
4023:
4022:
4017:
4002:
4001:
4000:
3995:
3990:
3985:
3974:
3972:
3963:
3957:
3956:
3954:
3953:
3948:
3943:
3942:
3941:
3931:
3926:
3925:
3924:
3914:
3913:
3912:
3907:
3902:
3892:
3887:
3882:
3881:
3880:
3875:
3870:
3854:
3853:
3852:
3847:
3842:
3832:
3831:
3830:
3825:
3815:
3814:
3813:
3803:
3802:
3801:
3791:
3786:
3781:
3775:
3773:
3763:
3762:
3750:
3749:
3746:
3745:
3742:
3741:
3739:
3738:
3733:
3728:
3723:
3717:
3715:
3709:
3708:
3706:
3705:
3700:
3695:
3689:
3687:
3683:
3682:
3680:
3679:
3674:
3669:
3664:
3659:
3654:
3649:
3643:
3641:
3635:
3634:
3632:
3631:
3629:Standard error
3626:
3621:
3616:
3615:
3614:
3609:
3598:
3596:
3590:
3589:
3587:
3586:
3581:
3576:
3571:
3566:
3561:
3559:Optimal design
3556:
3551:
3545:
3543:
3533:
3532:
3520:
3519:
3516:
3515:
3512:
3511:
3509:
3508:
3503:
3498:
3493:
3488:
3483:
3478:
3473:
3468:
3463:
3458:
3453:
3448:
3443:
3438:
3432:
3430:
3424:
3423:
3421:
3420:
3415:
3414:
3413:
3408:
3398:
3393:
3387:
3385:
3379:
3378:
3376:
3375:
3370:
3365:
3359:
3357:
3356:Summary tables
3353:
3352:
3350:
3349:
3343:
3341:
3335:
3334:
3331:
3330:
3328:
3327:
3326:
3325:
3320:
3315:
3305:
3299:
3297:
3291:
3290:
3288:
3287:
3282:
3277:
3272:
3267:
3262:
3257:
3251:
3249:
3243:
3242:
3240:
3239:
3234:
3229:
3228:
3227:
3222:
3217:
3212:
3207:
3202:
3197:
3192:
3190:Contraharmonic
3187:
3182:
3171:
3169:
3160:
3150:
3149:
3137:
3136:
3134:
3133:
3128:
3122:
3119:
3118:
3111:
3110:
3103:
3096:
3088:
3082:
3081:
3053:(3): 219â236.
3034:
3006:(4): 305â340.
2986:
2984:on 2013-02-02.
2968:
2954:E. L., Lehmann
2950:
2936:
2920:
2906:
2887:
2886:
2841:
2839:
2832:
2826:
2823:
2820:
2819:
2802:
2793:
2764:(1): 108â113.
2744:
2738:978-0534243128
2737:
2719:
2690:(1): 108â113.
2670:
2652:
2643:
2634:
2627:
2608:
2607:
2605:
2602:
2581:
2578:
2558:Basu's theorem
2550:
2549:Basu's theorem
2547:
2525:expected value
2499:occurs in the
2493:
2490:
2485:
2482:
2456:
2451:
2447:
2441:
2436:
2433:
2430:
2426:
2422:
2419:
2416:
2413:
2410:
2407:
2402:
2397:
2391:
2387:
2381:
2376:
2373:
2370:
2366:
2361:
2356:
2335:
2329:
2324:
2320:
2314:
2309:
2306:
2303:
2299:
2295:
2290:
2286:
2280:
2275:
2272:
2269:
2265:
2260:
2224:
2221:
2208:
2205:
2202:
2199:
2196:
2193:
2173:
2170:
2150:
2147:
2144:
2141:
2138:
2135:
2132:
2129:
2126:
2123:
2120:
2117:
2097:
2094:
2091:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2067:
2064:
2061:
2058:
2046:
2043:
2031:
2026:
2022:
2018:
2013:
2009:
1988:
1983:
1979:
1975:
1970:
1966:
1962:
1916:
1915:
1902:
1897:
1893:
1887:
1883:
1879:
1875:
1871:
1868:
1865:
1862:
1859:
1856:
1853:
1850:
1847:
1825:
1824:
1811:
1808:
1802:
1799:
1795:
1791:
1788:
1785:
1782:
1777:
1772:
1769:
1765:
1761:
1758:
1755:
1752:
1738:
1737:
1726:
1723:
1720:
1715:
1711:
1707:
1701:
1697:
1693:
1690:
1687:
1684:
1681:
1678:
1674:
1670:
1667:
1664:
1661:
1658:
1655:
1650:
1645:
1642:
1638:
1619:
1618:
1607:
1603:
1599:
1595:
1589:
1585:
1581:
1578:
1575:
1572:
1569:
1566:
1562:
1558:
1555:
1532:
1516:
1509:
1496:
1495:
1482:
1477:
1473:
1469:
1464:
1460:
1456:
1453:
1450:
1447:
1444:
1439:
1435:
1431:
1426:
1422:
1418:
1415:
1412:
1409:
1386:
1364:
1363:
1348:
1344:
1340:
1335:
1331:
1327:
1324:
1321:
1316:
1312:
1308:
1303:
1299:
1295:
1292:
1289:
1262:
1255:
1248:
1241:
1230:
1223:
1216:
1213:
1185:
1184:
1172:
1169:
1166:
1163:
1160:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1066:positive reals
1058:
1057:
1046:
1043:
1038:
1034:
1027:
1022:
1019:
1014:
1008:
1005:
1002:
999:
994:
989:
986:
983:
979:
952:
951:
940:
937:
932:
927:
921:
918:
915:
911:
906:
898:
893:
890:
885:
879:
876:
873:
870:
865:
860:
857:
854:
850:
826:
823:
820:
817:
814:
811:
808:
805:
800:
796:
776:
775:
764:
758:
753:
747:
744:
741:
737:
732:
724:
719:
716:
711:
705:
702:
699:
696:
690:
685:
682:
679:
675:
669:
665:
661:
658:
655:
652:
649:
643:
640:
637:
633:
629:
626:
623:
620:
615:
611:
604:
599:
596:
591:
585:
582:
579:
576:
570:
565:
562:
559:
555:
551:
548:
545:
542:
539:
536:
533:
530:
525:
521:
466:
462:
456:
451:
448:
445:
441:
437:
434:
407:
388:
385:
371:is said to be
367:The statistic
365:
364:
353:
350:
342:
339:
336:
333:
330:
327:
324:
321:
318:
315:
310:
305:
295:
287:
284:
281:
278:
275:
272:
269:
266:
263:
258:
254:
225:is said to be
221:The statistic
215:
208:
180:
161:
158:
146:sample dataset
144:computed on a
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
5432:
5421:
5418:
5417:
5415:
5400:
5399:
5390:
5388:
5387:
5378:
5376:
5375:
5370:
5364:
5362:
5361:
5352:
5351:
5348:
5334:
5331:
5329:
5328:Geostatistics
5326:
5324:
5321:
5319:
5316:
5314:
5311:
5310:
5308:
5306:
5302:
5296:
5295:Psychometrics
5293:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5266:
5263:
5261:
5258:
5256:
5253:
5251:
5248:
5247:
5245:
5243:
5239:
5233:
5230:
5228:
5225:
5223:
5219:
5216:
5214:
5211:
5209:
5206:
5204:
5201:
5200:
5198:
5196:
5192:
5186:
5183:
5181:
5178:
5176:
5172:
5169:
5167:
5164:
5163:
5161:
5159:
5158:Biostatistics
5155:
5151:
5147:
5142:
5138:
5120:
5119:Log-rank test
5117:
5116:
5114:
5110:
5104:
5101:
5100:
5098:
5096:
5092:
5086:
5083:
5081:
5078:
5076:
5073:
5071:
5068:
5067:
5065:
5063:
5059:
5056:
5054:
5050:
5040:
5037:
5035:
5032:
5030:
5027:
5025:
5022:
5020:
5017:
5016:
5014:
5012:
5008:
5002:
4999:
4997:
4994:
4992:
4990:(BoxâJenkins)
4986:
4984:
4981:
4979:
4976:
4972:
4969:
4968:
4967:
4964:
4963:
4961:
4959:
4955:
4949:
4946:
4944:
4943:DurbinâWatson
4941:
4939:
4933:
4931:
4928:
4926:
4925:DickeyâFuller
4923:
4922:
4920:
4916:
4910:
4907:
4905:
4902:
4900:
4899:Cointegration
4897:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4874:Decomposition
4872:
4871:
4869:
4865:
4862:
4860:
4856:
4846:
4843:
4842:
4841:
4838:
4837:
4836:
4833:
4829:
4826:
4825:
4824:
4821:
4819:
4816:
4814:
4811:
4809:
4806:
4804:
4801:
4799:
4796:
4794:
4791:
4789:
4786:
4785:
4783:
4781:
4777:
4771:
4768:
4766:
4763:
4761:
4758:
4756:
4753:
4751:
4748:
4746:
4745:Cohen's kappa
4743:
4742:
4740:
4738:
4734:
4730:
4726:
4722:
4718:
4714:
4709:
4705:
4691:
4688:
4686:
4683:
4681:
4678:
4676:
4673:
4672:
4670:
4668:
4664:
4658:
4654:
4650:
4644:
4642:
4639:
4638:
4636:
4634:
4630:
4624:
4621:
4619:
4616:
4614:
4611:
4609:
4606:
4604:
4601:
4599:
4598:Nonparametric
4596:
4594:
4591:
4590:
4588:
4584:
4578:
4575:
4573:
4570:
4568:
4565:
4563:
4560:
4559:
4557:
4555:
4551:
4545:
4542:
4540:
4537:
4535:
4532:
4530:
4527:
4525:
4522:
4521:
4519:
4517:
4513:
4507:
4504:
4502:
4499:
4497:
4494:
4492:
4489:
4488:
4486:
4484:
4480:
4476:
4469:
4466:
4464:
4461:
4460:
4456:
4452:
4436:
4433:
4432:
4431:
4428:
4426:
4423:
4421:
4418:
4414:
4411:
4409:
4406:
4405:
4404:
4401:
4400:
4398:
4396:
4392:
4382:
4379:
4375:
4369:
4367:
4361:
4359:
4353:
4352:
4351:
4348:
4347:Nonparametric
4345:
4343:
4337:
4333:
4330:
4329:
4328:
4322:
4318:
4317:Sample median
4315:
4314:
4313:
4310:
4309:
4307:
4305:
4301:
4293:
4290:
4288:
4285:
4283:
4280:
4279:
4278:
4275:
4273:
4270:
4268:
4262:
4260:
4257:
4255:
4252:
4250:
4247:
4245:
4242:
4240:
4238:
4234:
4232:
4229:
4228:
4226:
4224:
4220:
4214:
4212:
4208:
4206:
4204:
4199:
4197:
4192:
4188:
4187:
4184:
4181:
4179:
4175:
4165:
4162:
4160:
4157:
4155:
4152:
4151:
4149:
4147:
4143:
4137:
4134:
4130:
4127:
4126:
4125:
4122:
4118:
4115:
4114:
4113:
4110:
4108:
4105:
4104:
4102:
4100:
4096:
4088:
4085:
4083:
4080:
4079:
4078:
4075:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4050:
4049:
4047:
4045:
4041:
4035:
4032:
4028:
4025:
4021:
4018:
4016:
4013:
4012:
4011:
4008:
4007:
4006:
4003:
3999:
3996:
3994:
3991:
3989:
3986:
3984:
3981:
3980:
3979:
3976:
3975:
3973:
3971:
3967:
3964:
3962:
3958:
3952:
3949:
3947:
3944:
3940:
3937:
3936:
3935:
3932:
3930:
3927:
3923:
3922:loss function
3920:
3919:
3918:
3915:
3911:
3908:
3906:
3903:
3901:
3898:
3897:
3896:
3893:
3891:
3888:
3886:
3883:
3879:
3876:
3874:
3871:
3869:
3863:
3860:
3859:
3858:
3855:
3851:
3848:
3846:
3843:
3841:
3838:
3837:
3836:
3833:
3829:
3826:
3824:
3821:
3820:
3819:
3816:
3812:
3809:
3808:
3807:
3804:
3800:
3797:
3796:
3795:
3792:
3790:
3787:
3785:
3782:
3780:
3777:
3776:
3774:
3772:
3768:
3764:
3760:
3755:
3751:
3737:
3734:
3732:
3729:
3727:
3724:
3722:
3719:
3718:
3716:
3714:
3710:
3704:
3701:
3699:
3696:
3694:
3691:
3690:
3688:
3684:
3678:
3675:
3673:
3670:
3668:
3665:
3663:
3660:
3658:
3655:
3653:
3650:
3648:
3645:
3644:
3642:
3640:
3636:
3630:
3627:
3625:
3624:Questionnaire
3622:
3620:
3617:
3613:
3610:
3608:
3605:
3604:
3603:
3600:
3599:
3597:
3595:
3591:
3585:
3582:
3580:
3577:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3550:
3547:
3546:
3544:
3542:
3538:
3534:
3530:
3525:
3521:
3507:
3504:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3457:
3454:
3452:
3451:Control chart
3449:
3447:
3444:
3442:
3439:
3437:
3434:
3433:
3431:
3429:
3425:
3419:
3416:
3412:
3409:
3407:
3404:
3403:
3402:
3399:
3397:
3394:
3392:
3389:
3388:
3386:
3384:
3380:
3374:
3371:
3369:
3366:
3364:
3361:
3360:
3358:
3354:
3348:
3345:
3344:
3342:
3340:
3336:
3324:
3321:
3319:
3316:
3314:
3311:
3310:
3309:
3306:
3304:
3301:
3300:
3298:
3296:
3292:
3286:
3283:
3281:
3278:
3276:
3273:
3271:
3268:
3266:
3263:
3261:
3258:
3256:
3253:
3252:
3250:
3248:
3244:
3238:
3235:
3233:
3230:
3226:
3223:
3221:
3218:
3216:
3213:
3211:
3208:
3206:
3203:
3201:
3198:
3196:
3193:
3191:
3188:
3186:
3183:
3181:
3178:
3177:
3176:
3173:
3172:
3170:
3168:
3164:
3161:
3159:
3155:
3151:
3147:
3142:
3138:
3132:
3129:
3127:
3124:
3123:
3120:
3116:
3109:
3104:
3102:
3097:
3095:
3090:
3089:
3086:
3078:
3074:
3070:
3066:
3061:
3056:
3052:
3048:
3044:
3040:
3035:
3031:
3027:
3023:
3019:
3014:
3009:
3005:
3001:
3000:
2996:
2992:
2987:
2983:
2979:
2975:
2971:
2965:
2961:
2960:
2955:
2951:
2947:
2943:
2939:
2933:
2929:
2925:
2921:
2917:
2913:
2909:
2903:
2899:
2895:
2891:
2890:
2883:
2880:
2872:
2869:February 2012
2862:
2858:
2852:
2851:
2845:
2840:
2831:
2830:
2812:
2806:
2797:
2789:
2785:
2780:
2775:
2771:
2767:
2763:
2759:
2755:
2748:
2740:
2734:
2730:
2723:
2715:
2711:
2706:
2701:
2697:
2693:
2689:
2685:
2681:
2674:
2663:
2656:
2647:
2638:
2630:
2624:
2621:. CRC Press.
2620:
2613:
2609:
2601:
2598:
2594:
2590:
2586:
2577:
2575:
2571:
2567:
2563:
2559:
2555:
2546:
2544:
2539:
2537:
2533:
2528:
2526:
2522:
2518:
2514:
2510:
2506:
2502:
2498:
2489:
2481:
2479:
2474:
2472:
2454:
2449:
2445:
2439:
2434:
2431:
2428:
2424:
2417:
2414:
2411:
2405:
2400:
2395:
2389:
2385:
2379:
2374:
2371:
2368:
2364:
2359:
2354:
2333:
2327:
2322:
2318:
2312:
2307:
2304:
2301:
2297:
2293:
2288:
2284:
2278:
2273:
2270:
2267:
2263:
2258:
2249:
2245:
2241:
2237:
2232:
2230:
2220:
2203:
2200:
2194:
2191:
2171:
2168:
2148:
2145:
2136:
2133:
2127:
2124:
2118:
2095:
2089:
2086:
2083:
2080:
2077:
2074:
2071:
2065:
2062:
2059:
2056:
2042:
2029:
2024:
2020:
2016:
2011:
2007:
1981:
1977:
1973:
1968:
1964:
1951:
1949:
1945:
1941:
1937:
1933:
1929:
1925:
1921:
1900:
1895:
1891:
1885:
1881:
1877:
1873:
1866:
1860:
1857:
1851:
1845:
1838:
1837:
1836:
1834:
1830:
1809:
1806:
1800:
1797:
1793:
1786:
1780:
1767:
1763:
1756:
1750:
1743:
1742:
1741:
1724:
1721:
1718:
1713:
1709:
1705:
1699:
1691:
1688:
1685:
1682:
1676:
1672:
1668:
1665:
1659:
1653:
1640:
1636:
1628:
1627:
1626:
1624:
1605:
1601:
1597:
1593:
1587:
1579:
1576:
1573:
1570:
1564:
1560:
1556:
1553:
1546:
1545:
1544:
1530:
1522:
1515:
1512: +
1508:
1503:
1501:
1475:
1471:
1467:
1462:
1458:
1451:
1448:
1437:
1433:
1429:
1424:
1420:
1413:
1407:
1400:
1399:
1398:
1384:
1375:
1373:
1369:
1346:
1342:
1338:
1333:
1329:
1325:
1314:
1310:
1306:
1301:
1297:
1287:
1280:
1279:
1278:
1276:
1272:
1268:
1261:
1254:
1247:
1244: +
1240:
1236:
1229:
1222:
1212:
1210:
1206:
1202:
1198:
1194:
1190:
1170:
1164:
1161:
1158:
1152:
1149:
1143:
1137:
1130:
1129:
1128:
1126:
1122:
1118:
1114:
1110:
1106:
1102:
1097:
1095:
1091:
1087:
1083:
1079:
1075:
1071:
1067:
1063:
1044:
1041:
1036:
1032:
1020:
1017:
1003:
997:
992:
987:
984:
981:
977:
969:
968:
967:
965:
961:
957:
938:
935:
930:
925:
919:
916:
913:
909:
904:
891:
888:
874:
868:
863:
858:
855:
852:
848:
840:
839:
838:
824:
821:
812:
806:
798:
794:
785:
781:
762:
756:
751:
745:
742:
739:
735:
730:
717:
714:
700:
694:
688:
683:
680:
677:
673:
667:
659:
656:
653:
647:
641:
638:
635:
627:
624:
621:
613:
609:
597:
594:
580:
574:
568:
563:
560:
557:
553:
549:
540:
534:
528:
523:
511:
510:
509:
507:
503:
499:
495:
491:
488:which has a
487:
483:
464:
460:
454:
449:
446:
443:
439:
435:
432:
423:
419:
415:
412:has the same
410:
406:
402:
398:
397:random sample
394:
384:
382:
378:
374:
370:
351:
348:
340:
337:
331:
328:
322:
316:
308:
293:
285:
282:
273:
267:
261:
256:
239:
238:
237:
236:
232:
228:
224:
219:
214:
207:
203:
199:
195:
190:
188:
183:
179:
178:
174:
170:
167:
157:
155:
151:
147:
143:
139:
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: â
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
5396:
5384:
5365:
5358:
5270:Econometrics
5220: /
5203:Chemometrics
5180:Epidemiology
5173: /
5146:Applications
4988:ARIMA model
4935:Q-statistic
4884:Stationarity
4780:Multivariate
4723: /
4719: /
4717:Multivariate
4715: /
4655: /
4651: /
4425:Bayes factor
4324:Signed rank
4236:
4210:
4202:
4190:
3885:Completeness
3884:
3721:Cohort study
3619:Opinion poll
3554:Missing data
3541:Study design
3496:Scatter plot
3418:Scatter plot
3411:Spearman's Ď
3373:Grouped data
3050:
3046:
3003:
2997:
2982:the original
2958:
2927:
2897:
2875:
2866:
2847:
2805:
2796:
2761:
2757:
2747:
2728:
2722:
2687:
2683:
2673:
2655:
2646:
2637:
2618:
2612:
2584:
2583:
2561:
2553:
2552:
2540:
2535:
2532:not complete
2531:
2529:
2516:
2512:
2504:
2497:Completeness
2496:
2495:
2487:
2475:
2470:
2247:
2243:
2239:
2235:
2233:
2226:
2048:
1952:
1947:
1943:
1939:
1935:
1931:
1927:
1919:
1917:
1832:
1828:
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1504:
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1376:
1371:
1367:
1365:
1274:
1259:
1252:
1245:
1238:
1227:
1220:
1218:
1208:
1207:= 0 nor for
1204:
1200:
1196:
1192:
1188:
1186:
1124:
1120:
1116:
1112:
1108:
1104:
1100:
1098:
1093:
1089:
1085:
1081:
1073:
1069:
1061:
1059:
966:, one gets:
963:
959:
955:
954:On denoting
953:
783:
779:
777:
505:
501:
497:
493:
485:
481:
421:
417:
408:
404:
400:
392:
390:
380:
376:
372:
368:
366:
234:
230:
226:
222:
220:
212:
205:
193:
191:
186:
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176:
175:
168:
163:
138:completeness
137:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
5398:WikiProject
5313:Cartography
5275:Jurimetrics
5227:Reliability
4958:Time domain
4937:(LjungâBox)
4859:Time-series
4737:Categorical
4721:Time-series
4713:Categorical
4648:(Bernoulli)
4483:Correlation
4463:Correlation
4259:JarqueâBera
4231:Chi-squared
3993:M-estimator
3946:Asymptotics
3890:Sufficiency
3657:Interaction
3569:Replication
3549:Effect size
3506:Violin plot
3486:Radar chart
3466:Forest plot
3456:Correlogram
3406:Kendall's Ď
3039:ScheffĂŠ, H.
2991:ScheffĂŠ, H.
2861:introducing
2570:independent
1267:independent
164:Consider a
110:August 2009
5265:Demography
4983:ARMA model
4788:Regression
4365:(Friedman)
4326:(Wilcoxon)
4264:Normality
4254:Lilliefors
4201:Student's
4077:Resampling
3951:Robustness
3939:divergence
3929:Efficiency
3867:(monotone)
3862:Likelihood
3779:Population
3612:Stratified
3564:Population
3383:Dependence
3339:Count data
3270:Percentile
3247:Dispersion
3180:Arithmetic
3115:Statistics
2844:references
2825:References
2597:sufficient
2566:sufficient
2556:occurs in
2509:sufficient
1078:polynomial
1068:. Also, E(
160:Definition
134:statistics
80:newspapers
4646:Logistic
4413:posterior
4339:Rank sum
4087:Jackknife
4082:Bootstrap
3900:Bootstrap
3835:Parameter
3784:Statistic
3579:Statistic
3491:Run chart
3476:Pie chart
3471:Histogram
3461:Fan chart
3436:Bar chart
3318:L-moments
3205:Geometric
2541:See also
2425:∑
2406:−
2365:∑
2298:∑
2264:∑
2201:π
2195:
2169:θ
2134:π
2128:
2119:
2084:θ
2075:−
2072:θ
2066:
2060:∼
2017:−
1878:−
1801:θ
1776:∞
1771:∞
1768:−
1764:∫
1757:θ
1692:θ
1686:−
1677:−
1669:
1649:∞
1644:∞
1641:−
1637:∫
1580:θ
1574:−
1565:−
1557:
1162:−
978:∑
917:−
849:∑
743:−
674:∑
657:−
639:−
625:−
554:∑
529:
440:∑
349:θ
309:θ
294:θ
262:
257:θ
198:statistic
142:statistic
5414:Category
5360:Category
5053:Survival
4930:Johansen
4653:Binomial
4608:Isotonic
4195:(normal)
3840:location
3647:Blocking
3602:Sampling
3481:QâQ plot
3446:Box plot
3428:Graphics
3323:Skewness
3313:Kurtosis
3285:Variance
3215:Heronian
3210:Harmonic
3069:25048243
3041:(1955).
3022:25048038
2993:(1950).
2894:Basu, D.
2788:27499547
2714:27499547
2505:complete
2049:Suppose
1187:then, E(
1076:)) is a
399:of size
248:if
227:complete
5386:Commons
5333:Kriging
5218:Process
5175:studies
5034:Wavelet
4867:General
4034:Plug-in
3828:L space
3607:Cluster
3308:Moments
3126:Outline
3077:0072410
3030:0039201
2978:2135927
2946:0443141
2916:0953081
2857:improve
2779:4960505
2705:4960505
2572:of any
2063:Uniform
1226:,
1064:is the
94:scholar
5255:Census
4845:Normal
4793:Manova
4613:Robust
4363:2-way
4355:1-way
4193:-test
3864:
3441:Biplot
3232:Median
3225:Lehmer
3167:Center
3075:
3067:
3028:
3020:
2976:
2966:
2944:
2934:
2914:
2904:
2846:, but
2786:
2776:
2735:
2712:
2702:
2625:
2521:convex
1827:where
1265:) are
420:. Let
96:
89:
82:
75:
67:
4879:Trend
4408:prior
4350:anova
4239:-test
4213:-test
4205:-test
4112:Power
4057:Pivot
3850:shape
3845:scale
3295:Shape
3275:Range
3220:Heinz
3195:Cubic
3131:Index
3065:JSTOR
3018:JSTOR
2814:(PDF)
2665:(PDF)
2604:Notes
2184:Thus
2108:Then
1366:is a
1211:= 1.
962:) by
395:be a
211:,...,
196:is a
101:JSTOR
87:books
5112:Test
4312:Sign
4164:Wald
3237:Mode
3175:Mean
2964:ISBN
2932:ISBN
2902:ISBN
2784:PMID
2733:ISBN
2710:PMID
2623:ISBN
2564:and
2507:and
1370:for
192:Say
73:news
4292:BIC
4287:AIC
3055:doi
3008:doi
2774:PMC
2766:doi
2700:PMC
2692:doi
2568:is
2192:sin
2125:sin
1926:of
1666:exp
1554:exp
1165:0.5
1080:in
132:In
56:by
5416::
3073:MR
3071:.
3063:.
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3045:.
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2972:.
2942:MR
2940:.
2912:MR
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2782:.
2772:.
2762:70
2760:.
2756:.
2708:.
2698:.
2688:70
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235:g,
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2876:(
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2867:(
2853:.
2790:.
2768::
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2716:.
2694::
2667:.
2631:.
2536:θ
2517:θ
2513:θ
2471:θ
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2412:n
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2259:(
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2246:,
2244:θ
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2240:N
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2204:X
2198:(
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2149:0
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