4896:
4882:
4920:
4908:
119:(1948), which introduced U-statistics and set out the theory relating to them, and in doing so Sen outlines the importance U-statistics have in statistical theory. Sen says, âThe impact of Hoeffding (1948) is overwhelming at the present time and is very likely to continue in the years to come.â Note that the theory of U-statistics is not limited to the case of
108:
and that estimation of a certain parameter is required. Suppose that a simple unbiased estimate can be constructed based on only a few observations: this defines the basic estimator based on a given number of observations. For example, a single observation is itself an unbiased estimate of the mean
109:
and a pair of observations can be used to derive an unbiased estimate of the variance. The U-statistic based on this estimator is defined as the average (across all combinatorial selections of the given size from the full set of observations) of the basic estimator applied to the sub-samples.
746:
978:
38:
is a class of statistics defined as the average over the application of a given function applied to all tuples of a fixed size. The letter "U" stands for unbiased. In elementary statistics, U-statistics arise naturally in producing
1538:
2168:
values. However, it is a minimum variance unbiased estimate of the expected value of the median of three values, not the median of the population. Similar estimates play a central role where the parameters of a family of
522:
1985:
778:
1304:
1773:
2475:. Mathematics and its Applications. Vol. 273 (Translated by P. V. Malyshev and D. V. Malyshev from the 1989 Russian original ed.). Dordrecht: Kluwer Academic Publishers Group. pp. x+552.
2242:. Mathematics and its Applications. Vol. 273 (Translated by P. V. Malyshev and D. V. Malyshev from the 1989 Russian original ed.). Dordrecht: Kluwer Academic Publishers Group. pp. x+552.
1663:
417:
1392:
348:
2146:
77:: For example, for every probability distribution, the population median is an estimable parameter. The theory of U-statistics applies to general classes of probability distributions.
204:
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2015:
1825:
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1015:
450:
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1848:
770:
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263:
244:
224:
152:
1397:
741:{\displaystyle f_{n}(x_{1},\dotsc ,x_{n})={\frac {1}{\prod _{i=0}^{r-1}(n-i)}}\sum _{(i_{1},\dotsc ,i_{r})\in I_{r,n}}f(x_{i_{1}},\dotsc ,x_{i_{r}})}
2558:
4017:
1853:
4522:
973:{\displaystyle f_{n}(x_{1},\dotsc ,x_{n})={\frac {1}{\binom {n}{r}}}\sum _{(i_{1},\dotsc ,i_{r})\in J_{r,n}}f(x_{i_{1}},\dotsc ,x_{i_{r}})}
89:, the theory of U-statistics is used to establish for statistical procedures (such as estimators and tests) and estimators relating to the
4672:
85:
Many statistics originally derived for particular parametric families have been recognized as U-statistics for general distributions. In
4296:
2937:
1205:
2514:(1992) Introduction to Hoeffding (1948) A Class of Statistics with Asymptotically Normal Distribution. In: Kotz, S., Johnson, N. L.
1671:
4070:
4956:
4509:
93:
and to the variance (in finite samples) of such quantities. The theory has been used to study more general statistics as well as
2932:
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40:
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86:
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1103:
from a finite population, where the defining property is termed âinheritance on the averageâ.
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1994:
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987:
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2328:
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2257:
1060:
90:
2313:. Probability and its Applications. Boston, MA: BirkhÀuser Boston, Inc. pp. xvi+360.
1091:
U-statistics are very natural in statistical work, particularly in
Hoeffding's context of
8:
4886:
4811:
4734:
4415:
4179:
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70:
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1085:
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137:
94:
51:
31:
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116:
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3325:
3055:
2706:
2486:
2409:
2371:
2324:
2290:
2253:
1666:
4238:
1533:{\displaystyle f_{n}(x_{1},\ldots ,x_{n})=2/(n(n-1))\sum _{i>j}|x_{i}-x_{j}|}
4697:
4692:
3155:
3085:
2731:
2602:
2583:
4940:
4854:
4821:
4684:
4645:
4456:
4425:
3889:
3843:
3448:
3150:
2977:
2741:
2736:
2511:
2434:
2363:
112:
1133:, the U-statistic has the property that the average over sample values
4796:
4729:
4706:
4621:
3951:
3247:
3145:
3080:
3022:
3007:
2944:
2899:
2374:
2367:
98:
4839:
4801:
4484:
4385:
4247:
4060:
4027:
3519:
3436:
3075:
3032:
3012:
2992:
2982:
2751:
2579:
2186:
1980:{\displaystyle k_{3,n}(x)=\sum (x_{i}-{\bar {x}}_{n})^{3}n/((n-1)(n-2))}
3685:
3165:
2865:
2796:
2746:
2721:
2641:
2553:
2451:, 19:293â325. (Partially reprinted in: Kotz, S., Johnson, N. L. (1992)
2447:(1948) A class of statistics with asymptotically normal distributions.
131:
The term U-statistic, due to
Hoeffding (1948), is defined as follows.
3838:
3690:
3310:
3105:
3017:
3002:
2997:
2962:
2174:
3354:
2972:
2849:
2844:
2839:
1988:
4859:
4560:
1111:
4781:
3762:
3736:
3716:
2967:
2758:
2437:(1929) Moments and product moments of sampling distributions.
2083:
1299:{\displaystyle f_{n}(x)={\bar {x}}_{n}=(x_{1}+\cdots +x_{n})/n}
1768:{\displaystyle f_{n}(x)=\sum (x_{i}-{\bar {x}}_{n})^{2}/(n-1)}
2610:
2701:
2311:
Random series and stochastic integrals: Single and multiple
1093:
independent and identically distributed random variables
121:
independent and identically-distributed random variables
106:
independent and identically-distributed random variables
2173:
are being estimated by probability weighted moments or
2359:
Borovskikh's last chapter discusses U-statistics for
2154:
2092:
2026:
2020:
The following case highlights an important point. If
1997:
1856:
1836:
1807:
1781:
1674:
1575:
1546:
1400:
1315:
1208:
1173:
1063:
1023:
990:
781:
758:
525:
478:
458:
425:
356:
297:
271:
251:
232:
212:
160:
140:
4523:
Autoregressive conditional heteroskedasticity (ARCH)
3985:
2531:
2466:
2309:KwapieĆ, StanisÆaw; WoyczyĆski, Wojbor A. (1992).
2233:
2205:Cox & Hinkley (1974), p. 200, p. 258
2160:
2140:
2074:
2009:
1979:
1842:
1819:
1793:
1767:
1658:{\displaystyle f(x_{1},x_{2})=(x_{1}-x_{2})^{2}/2}
1657:
1558:
1532:
1386:
1298:
1194:
1076:
1042:
1009:
972:
764:
740:
508:
464:
444:
411:
342:
283:
257:
238:
218:
198:
146:
2534:Approximation theorems of mathematical statistics
2308:
1394:, the U-statistic is the mean pairwise deviation
4938:
1146:) is exactly equal to the population value
4071:Multivariate adaptive regression splines (MARS)
2559:Journal of the American Statistical Association
154:be either the real or complex numbers, and let
2439:Proceedings of the London Mathematical Society
412:{\displaystyle f(x_{i_{1}},\dotsc ,x_{i_{r}})}
2626:
850:
837:
2467:Koroljuk, V. S.; Borovskich, Yu. V. (1994).
2234:Koroljuk, V. S.; Borovskich, Yu. V. (1994).
1387:{\displaystyle f(x_{1},x_{2})=|x_{1}-x_{2}|}
503:
479:
343:{\displaystyle f_{n}\colon (K^{d})^{n}\to K}
350:is defined to be the average of the values
2671:
2633:
2619:
2390:
2271:
2141:{\displaystyle f_{n}(x_{1},\ldots ,x_{n})}
1118:U-statistics (Fisher, 1929; Tukey, 1950).
3284:
2601:
2214:Hoeffding (1948), between Eq's(4.3),(4.4)
115:(1992) provides a review of the paper by
2529:
772:is symmetric the above is simplified to
199:{\displaystyle f\colon (K^{d})^{r}\to K}
27:Class of statistics in estimation theory
14:
4939:
4597:KaplanâMeier estimator (product limit)
2578:
2518:, Vol I, pp 299â307. Springer-Verlag.
2455:, Vol I, pp 308â334. Springer-Verlag.
4670:
4237:
3984:
3283:
3053:
2670:
2614:
2552:
1129:taken from a population of size
4907:
4607:Accelerated failure time (AFT) model
2556:(1950). "Some Sampling Simplified".
2075:{\displaystyle f(x_{1},x_{2},x_{3})}
46:The theory of U-statistics allows a
41:minimum-variance unbiased estimators
4919:
4202:Analysis of variance (ANOVA, anova)
3054:
2584:"The Theory of Unbiased Estimation"
75:cumulative probability distribution
48:minimum-variance unbiased estimator
24:
4297:CochranâMantelâHaenszel statistics
2923:Pearson product-moment correlation
2420:Cox, D. R., Hinkley, D. V. (1974)
2398:. Utrecht: VSP. pp. xii+420.
2279:. Utrecht: VSP. pp. xii+420.
841:
25:
4973:
2589:Annals of Mathematical Statistics
2538:. New York: John Wiley and Sons.
2501:. Marcel Dekker, New York. pp320
2499:U-Statistics: Theory and Practice
516:with distinct entries. Formally,
509:{\displaystyle \{1,2,\dotsc ,n\}}
265:-dimensional variables. For each
4918:
4906:
4894:
4881:
4880:
4671:
104:Suppose that a problem involves
4556:Least-squares spectral analysis
123:or to scalar random-variables.
4957:Asymptotic theory (statistics)
3537:Mean-unbiased minimum-variance
2640:
2572:10.1080/01621459.1950.10501142
2353:
2344:
2335:
2301:
2264:
2226:
2217:
2208:
2199:
2135:
2103:
2069:
2030:
1974:
1971:
1959:
1956:
1944:
1941:
1924:
1911:
1888:
1879:
1873:
1762:
1750:
1736:
1723:
1700:
1691:
1685:
1638:
1611:
1605:
1579:
1526:
1498:
1478:
1475:
1463:
1457:
1443:
1411:
1380:
1352:
1345:
1319:
1285:
1253:
1238:
1225:
1219:
1183:
1177:
967:
921:
894:
862:
824:
792:
735:
689:
662:
630:
619:
607:
568:
536:
406:
360:
334:
325:
311:
190:
181:
167:
69:. An estimable parameter is a
13:
1:
4850:Geographic information system
4066:Simultaneous equations models
2384:
126:
4033:Coefficient of determination
3644:Uniformly most powerful test
2530:Serfling, Robert J. (1980).
2396:-statistics in Banach spaces
2277:-statistics in Banach spaces
7:
4602:Proportional hazards models
4546:Spectral density estimation
4528:Vector autoregression (VAR)
3962:Maximum posterior estimator
3194:Randomized controlled trial
2516:Breakthroughs in Statistics
2453:Breakthroughs in Statistics
2391:Borovskikh, Yu. V. (1996).
2272:Borovskikh, Yu. V. (1996).
2180:
1162:
1121:For a simple random sample
291:the associated U-statistic
10:
4978:
4362:Multivariate distributions
2782:Average absolute deviation
80:
4876:
4830:
4767:
4720:
4683:
4679:
4666:
4638:
4620:
4587:
4578:
4536:
4483:
4444:
4393:
4384:
4350:Structural equation model
4305:
4262:
4258:
4233:
4192:
4158:
4112:
4079:
4041:
4008:
4004:
3980:
3920:
3829:
3748:
3712:
3703:
3686:Score/Lagrange multiplier
3671:
3624:
3569:
3495:
3486:
3296:
3292:
3279:
3238:
3212:
3164:
3119:
3101:Sample size determination
3066:
3062:
3049:
2953:
2908:
2882:
2864:
2820:
2772:
2692:
2683:
2679:
2666:
2648:
2171:probability distributions
1665:, the U-statistic is the
87:non-parametric statistics
67:probability distributions
4952:Nonparametric statistics
4845:Environmental statistics
4367:Elliptical distributions
4160:Generalized linear model
4089:Simple linear regression
3859:HodgesâLehmann estimator
3316:Probability distribution
3225:Stochastic approximation
2787:Coefficient of variation
2192:
1110:-statistics and Tukey's
1095:, or more generally for
472:-tuples of indices from
50:to be derived from each
4505:Cross-correlation (XCF)
4113:Non-standard predictors
3547:LehmannâScheffĂ© theorem
3220:Adaptive clinical trial
2603:10.1214/aoms/1177731020
2010:{\displaystyle n\geq 3}
1820:{\displaystyle n\geq 2}
1559:{\displaystyle n\geq 2}
1043:{\displaystyle I_{r,n}}
1010:{\displaystyle J_{r,n}}
445:{\displaystyle I_{r,n}}
284:{\displaystyle n\geq r}
65:) for large classes of
4901:Mathematics portal
4722:Engineering statistics
4630:NelsonâAalen estimator
4207:Analysis of covariance
4094:Ordinary least squares
4018:Pearson product-moment
3422:Statistical functional
3333:Empirical distribution
3166:Controlled experiments
2895:Frequency distribution
2673:Descriptive statistics
2441:, 2, 30:199–238.
2422:Theoretical statistics
2341:Sen (1992) p. 307
2162:
2142:
2076:
2011:
1981:
1844:
1821:
1795:
1769:
1659:
1560:
1534:
1388:
1300:
1196:
1195:{\displaystyle f(x)=x}
1116:homogeneous polynomial
1101:simple random sampling
1097:exchangeable sequences
1078:
1044:
1017:denotes the subset of
1011:
974:
766:
742:
606:
510:
466:
446:
413:
344:
285:
259:
240:
220:
200:
148:
4817:Population statistics
4759:System identification
4493:Autocorrelation (ACF)
4421:Exponential smoothing
4335:Discriminant analysis
4330:Canonical correlation
4194:Partition of variance
4056:Regression validation
3900:(JonckheereâTerpstra)
3799:Likelihood-ratio test
3488:Frequentist inference
3400:Locationâscale family
3321:Sampling distribution
3286:Statistical inference
3253:Cross-sectional study
3240:Observational studies
3199:Randomized experiment
3028:Stem-and-leaf display
2830:Central limit theorem
2163:
2148:is not the median of
2143:
2077:
2012:
1982:
1845:
1822:
1796:
1770:
1660:
1561:
1535:
1389:
1301:
1197:
1079:
1077:{\displaystyle f_{n}}
1045:
1012:
975:
767:
743:
580:
511:
467:
447:
414:
345:
286:
260:
241:
221:
201:
149:
4740:Probabilistic design
4325:Principal components
4168:Exponential families
4120:Nonlinear regression
4099:General linear model
4061:Mixed effects models
4051:Errors and residuals
4028:Confounding variable
3930:Bayesian probability
3908:Van der Waerden test
3898:Ordered alternative
3663:Multiple comparisons
3542:RaoâBlackwellization
3505:Estimating equations
3461:Statistical distance
3179:Factorial experiment
2712:Arithmetic-Geometric
2449:Annals of Statistics
2424:. Chapman and Hall.
2152:
2090:
2024:
2017:, is a U-statistic.
1995:
1854:
1834:
1805:
1779:
1672:
1573:
1544:
1398:
1313:
1306:is the sample mean.
1206:
1171:
1061:
1021:
988:
779:
756:
523:
476:
456:
423:
354:
295:
269:
249:
230:
226:-valued function of
210:
158:
138:
95:stochastic processes
91:asymptotic normality
73:of the population's
4812:Official statistics
4735:Methods engineering
4416:Seasonal adjustment
4184:Poisson regressions
4104:Bayesian regression
4043:Regression analysis
4023:Partial correlation
3995:Regression analysis
3594:Prediction interval
3589:Likelihood interval
3579:Confidence interval
3571:Interval estimation
3532:Unbiased estimators
3350:Model specification
3230:Up-and-down designs
2918:Partial correlation
2874:Index of dispersion
2792:Interquartile range
2366:taking values in a
1794:{\displaystyle n-1}
71:measurable function
56:estimable parameter
4832:Spatial statistics
4712:Medical statistics
4612:First hitting time
4566:Whittle likelihood
4217:Degrees of freedom
4212:Multivariate ANOVA
4145:Heteroscedasticity
3957:Bayesian estimator
3922:Bayesian inference
3771:KolmogorovâSmirnov
3656:Randomization test
3626:Testing hypotheses
3599:Tolerance interval
3510:Maximum likelihood
3405:Exponential family
3338:Density estimation
3298:Statistical theory
3258:Natural experiment
3204:Scientific control
3121:Survey methodology
2807:Standard deviation
2497:Lee, A. J. (1990)
2158:
2138:
2072:
2007:
1977:
1840:
1817:
1791:
1765:
1655:
1556:
1530:
1496:
1384:
1296:
1192:
1167:Some examples: If
1086:symmetric function
1074:
1040:
1007:
970:
917:
762:
752:In particular, if
738:
685:
506:
462:
442:
409:
340:
281:
255:
236:
216:
196:
144:
52:unbiased estimator
32:statistical theory
4947:Estimation theory
4934:
4933:
4872:
4871:
4868:
4867:
4807:National accounts
4777:Actuarial science
4769:Social statistics
4662:
4661:
4658:
4657:
4654:
4653:
4589:Survival function
4574:
4573:
4436:Granger causality
4277:Contingency table
4252:Survival analysis
4229:
4228:
4225:
4224:
4081:Linear regression
3976:
3975:
3972:
3971:
3947:Credible interval
3916:
3915:
3699:
3698:
3515:Method of moments
3384:Parametric family
3345:Statistical model
3275:
3274:
3271:
3270:
3189:Random assignment
3111:Statistical power
3045:
3044:
3041:
3040:
2890:Contingency table
2860:
2859:
2727:Generalized/power
2270:Pages 381â382 in
2161:{\displaystyle n}
2086:of three values,
1914:
1843:{\displaystyle k}
1726:
1481:
1241:
1084:is necessarily a
1057:Each U-statistic
857:
855:
848:
765:{\displaystyle f}
625:
623:
465:{\displaystyle r}
258:{\displaystyle d}
239:{\displaystyle r}
219:{\displaystyle K}
147:{\displaystyle K}
117:Wassily Hoeffding
16:(Redirected from
4969:
4922:
4921:
4910:
4909:
4899:
4898:
4884:
4883:
4787:Crime statistics
4681:
4680:
4668:
4667:
4585:
4584:
4551:Fourier analysis
4538:Frequency domain
4518:
4465:
4431:Structural break
4391:
4390:
4340:Cluster analysis
4287:Log-linear model
4260:
4259:
4235:
4234:
4176:
4150:Homoscedasticity
4006:
4005:
3982:
3981:
3901:
3893:
3885:
3884:(KruskalâWallis)
3869:
3854:
3809:Cross validation
3794:
3776:AndersonâDarling
3723:
3710:
3709:
3681:Likelihood-ratio
3673:Parametric tests
3651:Permutation test
3634:1- & 2-tails
3525:Minimum distance
3497:Point estimation
3493:
3492:
3444:Optimal decision
3395:
3294:
3293:
3281:
3280:
3263:Quasi-experiment
3213:Adaptive designs
3064:
3063:
3051:
3050:
2928:Rank correlation
2690:
2689:
2681:
2680:
2668:
2667:
2635:
2628:
2621:
2612:
2611:
2607:
2605:
2575:
2566:(252): 501â519.
2549:
2537:
2494:
2417:
2378:
2357:
2351:
2350:Sen (1992), p306
2348:
2342:
2339:
2333:
2332:
2305:
2299:
2298:
2268:
2262:
2261:
2230:
2224:
2221:
2215:
2212:
2206:
2203:
2167:
2165:
2164:
2159:
2147:
2145:
2144:
2139:
2134:
2133:
2115:
2114:
2102:
2101:
2081:
2079:
2078:
2073:
2068:
2067:
2055:
2054:
2042:
2041:
2016:
2014:
2013:
2008:
1986:
1984:
1983:
1978:
1940:
1932:
1931:
1922:
1921:
1916:
1915:
1907:
1900:
1899:
1872:
1871:
1849:
1847:
1846:
1841:
1826:
1824:
1823:
1818:
1800:
1798:
1797:
1792:
1774:
1772:
1771:
1766:
1749:
1744:
1743:
1734:
1733:
1728:
1727:
1719:
1712:
1711:
1684:
1683:
1664:
1662:
1661:
1656:
1651:
1646:
1645:
1636:
1635:
1623:
1622:
1604:
1603:
1591:
1590:
1565:
1563:
1562:
1557:
1539:
1537:
1536:
1531:
1529:
1524:
1523:
1511:
1510:
1501:
1495:
1456:
1442:
1441:
1423:
1422:
1410:
1409:
1393:
1391:
1390:
1385:
1383:
1378:
1377:
1365:
1364:
1355:
1344:
1343:
1331:
1330:
1305:
1303:
1302:
1297:
1292:
1284:
1283:
1265:
1264:
1249:
1248:
1243:
1242:
1234:
1218:
1217:
1202:the U-statistic
1201:
1199:
1198:
1193:
1114:are examples of
1083:
1081:
1080:
1075:
1073:
1072:
1049:
1047:
1046:
1041:
1039:
1038:
1016:
1014:
1013:
1008:
1006:
1005:
979:
977:
976:
971:
966:
965:
964:
963:
940:
939:
938:
937:
916:
915:
914:
893:
892:
874:
873:
856:
854:
853:
840:
831:
823:
822:
804:
803:
791:
790:
771:
769:
768:
763:
747:
745:
744:
739:
734:
733:
732:
731:
708:
707:
706:
705:
684:
683:
682:
661:
660:
642:
641:
624:
622:
605:
594:
575:
567:
566:
548:
547:
535:
534:
515:
513:
512:
507:
471:
469:
468:
463:
451:
449:
448:
443:
441:
440:
418:
416:
415:
410:
405:
404:
403:
402:
379:
378:
377:
376:
349:
347:
346:
341:
333:
332:
323:
322:
307:
306:
290:
288:
287:
282:
264:
262:
261:
256:
245:
243:
242:
237:
225:
223:
222:
217:
205:
203:
202:
197:
189:
188:
179:
178:
153:
151:
150:
145:
58:(alternatively,
21:
4977:
4976:
4972:
4971:
4970:
4968:
4967:
4966:
4937:
4936:
4935:
4930:
4893:
4864:
4826:
4763:
4749:quality control
4716:
4698:Clinical trials
4675:
4650:
4634:
4622:Hazard function
4616:
4570:
4532:
4516:
4479:
4475:BreuschâGodfrey
4463:
4440:
4380:
4355:Factor analysis
4301:
4282:Graphical model
4254:
4221:
4188:
4174:
4154:
4108:
4075:
4037:
4000:
3999:
3968:
3912:
3899:
3891:
3883:
3867:
3852:
3831:Rank statistics
3825:
3804:Model selection
3792:
3750:Goodness of fit
3744:
3721:
3695:
3667:
3620:
3565:
3554:Median unbiased
3482:
3393:
3326:Order statistic
3288:
3267:
3234:
3208:
3160:
3115:
3058:
3056:Data collection
3037:
2949:
2904:
2878:
2856:
2816:
2768:
2685:Continuous data
2675:
2662:
2644:
2639:
2546:
2483:
2406:
2387:
2382:
2381:
2364:random elements
2358:
2354:
2349:
2345:
2340:
2336:
2321:
2306:
2302:
2287:
2269:
2265:
2250:
2231:
2227:
2222:
2218:
2213:
2209:
2204:
2200:
2195:
2183:
2153:
2150:
2149:
2129:
2125:
2110:
2106:
2097:
2093:
2091:
2088:
2087:
2063:
2059:
2050:
2046:
2037:
2033:
2025:
2022:
2021:
1996:
1993:
1992:
1936:
1927:
1923:
1917:
1906:
1905:
1904:
1895:
1891:
1861:
1857:
1855:
1852:
1851:
1835:
1832:
1831:
1806:
1803:
1802:
1780:
1777:
1776:
1745:
1739:
1735:
1729:
1718:
1717:
1716:
1707:
1703:
1679:
1675:
1673:
1670:
1669:
1667:sample variance
1647:
1641:
1637:
1631:
1627:
1618:
1614:
1599:
1595:
1586:
1582:
1574:
1571:
1570:
1545:
1542:
1541:
1525:
1519:
1515:
1506:
1502:
1497:
1485:
1452:
1437:
1433:
1418:
1414:
1405:
1401:
1399:
1396:
1395:
1379:
1373:
1369:
1360:
1356:
1351:
1339:
1335:
1326:
1322:
1314:
1311:
1310:
1288:
1279:
1275:
1260:
1256:
1244:
1233:
1232:
1231:
1213:
1209:
1207:
1204:
1203:
1172:
1169:
1168:
1165:
1154:
1141:
1068:
1064:
1062:
1059:
1058:
1028:
1024:
1022:
1019:
1018:
995:
991:
989:
986:
985:
959:
955:
954:
950:
933:
929:
928:
924:
904:
900:
888:
884:
869:
865:
861:
849:
836:
835:
830:
818:
814:
799:
795:
786:
782:
780:
777:
776:
757:
754:
753:
727:
723:
722:
718:
701:
697:
696:
692:
672:
668:
656:
652:
637:
633:
629:
595:
584:
579:
574:
562:
558:
543:
539:
530:
526:
524:
521:
520:
477:
474:
473:
457:
454:
453:
430:
426:
424:
421:
420:
398:
394:
393:
389:
372:
368:
367:
363:
355:
352:
351:
328:
324:
318:
314:
302:
298:
296:
293:
292:
270:
267:
266:
250:
247:
246:
231:
228:
227:
211:
208:
207:
184:
180:
174:
170:
159:
156:
155:
139:
136:
135:
129:
83:
28:
23:
22:
15:
12:
11:
5:
4975:
4965:
4964:
4959:
4954:
4949:
4932:
4931:
4929:
4928:
4916:
4904:
4890:
4877:
4874:
4873:
4870:
4869:
4866:
4865:
4863:
4862:
4857:
4852:
4847:
4842:
4836:
4834:
4828:
4827:
4825:
4824:
4819:
4814:
4809:
4804:
4799:
4794:
4789:
4784:
4779:
4773:
4771:
4765:
4764:
4762:
4761:
4756:
4751:
4742:
4737:
4732:
4726:
4724:
4718:
4717:
4715:
4714:
4709:
4704:
4695:
4693:Bioinformatics
4689:
4687:
4677:
4676:
4664:
4663:
4660:
4659:
4656:
4655:
4652:
4651:
4649:
4648:
4642:
4640:
4636:
4635:
4633:
4632:
4626:
4624:
4618:
4617:
4615:
4614:
4609:
4604:
4599:
4593:
4591:
4582:
4576:
4575:
4572:
4571:
4569:
4568:
4563:
4558:
4553:
4548:
4542:
4540:
4534:
4533:
4531:
4530:
4525:
4520:
4512:
4507:
4502:
4501:
4500:
4498:partial (PACF)
4489:
4487:
4481:
4480:
4478:
4477:
4472:
4467:
4459:
4454:
4448:
4446:
4445:Specific tests
4442:
4441:
4439:
4438:
4433:
4428:
4423:
4418:
4413:
4408:
4403:
4397:
4395:
4388:
4382:
4381:
4379:
4378:
4377:
4376:
4375:
4374:
4359:
4358:
4357:
4347:
4345:Classification
4342:
4337:
4332:
4327:
4322:
4317:
4311:
4309:
4303:
4302:
4300:
4299:
4294:
4292:McNemar's test
4289:
4284:
4279:
4274:
4268:
4266:
4256:
4255:
4231:
4230:
4227:
4226:
4223:
4222:
4220:
4219:
4214:
4209:
4204:
4198:
4196:
4190:
4189:
4187:
4186:
4170:
4164:
4162:
4156:
4155:
4153:
4152:
4147:
4142:
4137:
4132:
4130:Semiparametric
4127:
4122:
4116:
4114:
4110:
4109:
4107:
4106:
4101:
4096:
4091:
4085:
4083:
4077:
4076:
4074:
4073:
4068:
4063:
4058:
4053:
4047:
4045:
4039:
4038:
4036:
4035:
4030:
4025:
4020:
4014:
4012:
4002:
4001:
3998:
3997:
3992:
3986:
3978:
3977:
3974:
3973:
3970:
3969:
3967:
3966:
3965:
3964:
3954:
3949:
3944:
3943:
3942:
3937:
3926:
3924:
3918:
3917:
3914:
3913:
3911:
3910:
3905:
3904:
3903:
3895:
3887:
3871:
3868:(MannâWhitney)
3863:
3862:
3861:
3848:
3847:
3846:
3835:
3833:
3827:
3826:
3824:
3823:
3822:
3821:
3816:
3811:
3801:
3796:
3793:(ShapiroâWilk)
3788:
3783:
3778:
3773:
3768:
3760:
3754:
3752:
3746:
3745:
3743:
3742:
3734:
3725:
3713:
3707:
3705:Specific tests
3701:
3700:
3697:
3696:
3694:
3693:
3688:
3683:
3677:
3675:
3669:
3668:
3666:
3665:
3660:
3659:
3658:
3648:
3647:
3646:
3636:
3630:
3628:
3622:
3621:
3619:
3618:
3617:
3616:
3611:
3601:
3596:
3591:
3586:
3581:
3575:
3573:
3567:
3566:
3564:
3563:
3558:
3557:
3556:
3551:
3550:
3549:
3544:
3529:
3528:
3527:
3522:
3517:
3512:
3501:
3499:
3490:
3484:
3483:
3481:
3480:
3475:
3470:
3469:
3468:
3458:
3453:
3452:
3451:
3441:
3440:
3439:
3434:
3429:
3419:
3414:
3409:
3408:
3407:
3402:
3397:
3381:
3380:
3379:
3374:
3369:
3359:
3358:
3357:
3352:
3342:
3341:
3340:
3330:
3329:
3328:
3318:
3313:
3308:
3302:
3300:
3290:
3289:
3277:
3276:
3273:
3272:
3269:
3268:
3266:
3265:
3260:
3255:
3250:
3244:
3242:
3236:
3235:
3233:
3232:
3227:
3222:
3216:
3214:
3210:
3209:
3207:
3206:
3201:
3196:
3191:
3186:
3181:
3176:
3170:
3168:
3162:
3161:
3159:
3158:
3156:Standard error
3153:
3148:
3143:
3142:
3141:
3136:
3125:
3123:
3117:
3116:
3114:
3113:
3108:
3103:
3098:
3093:
3088:
3086:Optimal design
3083:
3078:
3072:
3070:
3060:
3059:
3047:
3046:
3043:
3042:
3039:
3038:
3036:
3035:
3030:
3025:
3020:
3015:
3010:
3005:
3000:
2995:
2990:
2985:
2980:
2975:
2970:
2965:
2959:
2957:
2951:
2950:
2948:
2947:
2942:
2941:
2940:
2935:
2925:
2920:
2914:
2912:
2906:
2905:
2903:
2902:
2897:
2892:
2886:
2884:
2883:Summary tables
2880:
2879:
2877:
2876:
2870:
2868:
2862:
2861:
2858:
2857:
2855:
2854:
2853:
2852:
2847:
2842:
2832:
2826:
2824:
2818:
2817:
2815:
2814:
2809:
2804:
2799:
2794:
2789:
2784:
2778:
2776:
2770:
2769:
2767:
2766:
2761:
2756:
2755:
2754:
2749:
2744:
2739:
2734:
2729:
2724:
2719:
2717:Contraharmonic
2714:
2709:
2698:
2696:
2687:
2677:
2676:
2664:
2663:
2661:
2660:
2655:
2649:
2646:
2645:
2638:
2637:
2630:
2623:
2615:
2609:
2608:
2576:
2550:
2544:
2527:
2509:
2495:
2481:
2464:
2442:
2432:
2418:
2404:
2386:
2383:
2380:
2379:
2352:
2343:
2334:
2319:
2300:
2285:
2263:
2248:
2225:
2216:
2207:
2197:
2196:
2194:
2191:
2190:
2189:
2182:
2179:
2157:
2137:
2132:
2128:
2124:
2121:
2118:
2113:
2109:
2105:
2100:
2096:
2071:
2066:
2062:
2058:
2053:
2049:
2045:
2040:
2036:
2032:
2029:
2006:
2003:
2000:
1976:
1973:
1970:
1967:
1964:
1961:
1958:
1955:
1952:
1949:
1946:
1943:
1939:
1935:
1930:
1926:
1920:
1913:
1910:
1903:
1898:
1894:
1890:
1887:
1884:
1881:
1878:
1875:
1870:
1867:
1864:
1860:
1839:
1816:
1813:
1810:
1801:, defined for
1790:
1787:
1784:
1764:
1761:
1758:
1755:
1752:
1748:
1742:
1738:
1732:
1725:
1722:
1715:
1710:
1706:
1702:
1699:
1696:
1693:
1690:
1687:
1682:
1678:
1654:
1650:
1644:
1640:
1634:
1630:
1626:
1621:
1617:
1613:
1610:
1607:
1602:
1598:
1594:
1589:
1585:
1581:
1578:
1555:
1552:
1549:
1540:, defined for
1528:
1522:
1518:
1514:
1509:
1505:
1500:
1494:
1491:
1488:
1484:
1480:
1477:
1474:
1471:
1468:
1465:
1462:
1459:
1455:
1451:
1448:
1445:
1440:
1436:
1432:
1429:
1426:
1421:
1417:
1413:
1408:
1404:
1382:
1376:
1372:
1368:
1363:
1359:
1354:
1350:
1347:
1342:
1338:
1334:
1329:
1325:
1321:
1318:
1295:
1291:
1287:
1282:
1278:
1274:
1271:
1268:
1263:
1259:
1255:
1252:
1247:
1240:
1237:
1230:
1227:
1224:
1221:
1216:
1212:
1191:
1188:
1185:
1182:
1179:
1176:
1164:
1161:
1150:
1137:
1071:
1067:
1037:
1034:
1031:
1027:
1004:
1001:
998:
994:
982:
981:
969:
962:
958:
953:
949:
946:
943:
936:
932:
927:
923:
920:
913:
910:
907:
903:
899:
896:
891:
887:
883:
880:
877:
872:
868:
864:
860:
852:
847:
844:
839:
834:
829:
826:
821:
817:
813:
810:
807:
802:
798:
794:
789:
785:
761:
750:
749:
737:
730:
726:
721:
717:
714:
711:
704:
700:
695:
691:
688:
681:
678:
675:
671:
667:
664:
659:
655:
651:
648:
645:
640:
636:
632:
628:
621:
618:
615:
612:
609:
604:
601:
598:
593:
590:
587:
583:
578:
573:
570:
565:
561:
557:
554:
551:
546:
542:
538:
533:
529:
505:
502:
499:
496:
493:
490:
487:
484:
481:
461:
439:
436:
433:
429:
408:
401:
397:
392:
388:
385:
382:
375:
371:
366:
362:
359:
339:
336:
331:
327:
321:
317:
313:
310:
305:
301:
280:
277:
274:
254:
235:
215:
195:
192:
187:
183:
177:
173:
169:
166:
163:
143:
128:
125:
82:
79:
26:
9:
6:
4:
3:
2:
4974:
4963:
4960:
4958:
4955:
4953:
4950:
4948:
4945:
4944:
4942:
4927:
4926:
4917:
4915:
4914:
4905:
4903:
4902:
4897:
4891:
4889:
4888:
4879:
4878:
4875:
4861:
4858:
4856:
4855:Geostatistics
4853:
4851:
4848:
4846:
4843:
4841:
4838:
4837:
4835:
4833:
4829:
4823:
4822:Psychometrics
4820:
4818:
4815:
4813:
4810:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4783:
4780:
4778:
4775:
4774:
4772:
4770:
4766:
4760:
4757:
4755:
4752:
4750:
4746:
4743:
4741:
4738:
4736:
4733:
4731:
4728:
4727:
4725:
4723:
4719:
4713:
4710:
4708:
4705:
4703:
4699:
4696:
4694:
4691:
4690:
4688:
4686:
4685:Biostatistics
4682:
4678:
4674:
4669:
4665:
4647:
4646:Log-rank test
4644:
4643:
4641:
4637:
4631:
4628:
4627:
4625:
4623:
4619:
4613:
4610:
4608:
4605:
4603:
4600:
4598:
4595:
4594:
4592:
4590:
4586:
4583:
4581:
4577:
4567:
4564:
4562:
4559:
4557:
4554:
4552:
4549:
4547:
4544:
4543:
4541:
4539:
4535:
4529:
4526:
4524:
4521:
4519:
4517:(BoxâJenkins)
4513:
4511:
4508:
4506:
4503:
4499:
4496:
4495:
4494:
4491:
4490:
4488:
4486:
4482:
4476:
4473:
4471:
4470:DurbinâWatson
4468:
4466:
4460:
4458:
4455:
4453:
4452:DickeyâFuller
4450:
4449:
4447:
4443:
4437:
4434:
4432:
4429:
4427:
4426:Cointegration
4424:
4422:
4419:
4417:
4414:
4412:
4409:
4407:
4404:
4402:
4401:Decomposition
4399:
4398:
4396:
4392:
4389:
4387:
4383:
4373:
4370:
4369:
4368:
4365:
4364:
4363:
4360:
4356:
4353:
4352:
4351:
4348:
4346:
4343:
4341:
4338:
4336:
4333:
4331:
4328:
4326:
4323:
4321:
4318:
4316:
4313:
4312:
4310:
4308:
4304:
4298:
4295:
4293:
4290:
4288:
4285:
4283:
4280:
4278:
4275:
4273:
4272:Cohen's kappa
4270:
4269:
4267:
4265:
4261:
4257:
4253:
4249:
4245:
4241:
4236:
4232:
4218:
4215:
4213:
4210:
4208:
4205:
4203:
4200:
4199:
4197:
4195:
4191:
4185:
4181:
4177:
4171:
4169:
4166:
4165:
4163:
4161:
4157:
4151:
4148:
4146:
4143:
4141:
4138:
4136:
4133:
4131:
4128:
4126:
4125:Nonparametric
4123:
4121:
4118:
4117:
4115:
4111:
4105:
4102:
4100:
4097:
4095:
4092:
4090:
4087:
4086:
4084:
4082:
4078:
4072:
4069:
4067:
4064:
4062:
4059:
4057:
4054:
4052:
4049:
4048:
4046:
4044:
4040:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4016:
4015:
4013:
4011:
4007:
4003:
3996:
3993:
3991:
3988:
3987:
3983:
3979:
3963:
3960:
3959:
3958:
3955:
3953:
3950:
3948:
3945:
3941:
3938:
3936:
3933:
3932:
3931:
3928:
3927:
3925:
3923:
3919:
3909:
3906:
3902:
3896:
3894:
3888:
3886:
3880:
3879:
3878:
3875:
3874:Nonparametric
3872:
3870:
3864:
3860:
3857:
3856:
3855:
3849:
3845:
3844:Sample median
3842:
3841:
3840:
3837:
3836:
3834:
3832:
3828:
3820:
3817:
3815:
3812:
3810:
3807:
3806:
3805:
3802:
3800:
3797:
3795:
3789:
3787:
3784:
3782:
3779:
3777:
3774:
3772:
3769:
3767:
3765:
3761:
3759:
3756:
3755:
3753:
3751:
3747:
3741:
3739:
3735:
3733:
3731:
3726:
3724:
3719:
3715:
3714:
3711:
3708:
3706:
3702:
3692:
3689:
3687:
3684:
3682:
3679:
3678:
3676:
3674:
3670:
3664:
3661:
3657:
3654:
3653:
3652:
3649:
3645:
3642:
3641:
3640:
3637:
3635:
3632:
3631:
3629:
3627:
3623:
3615:
3612:
3610:
3607:
3606:
3605:
3602:
3600:
3597:
3595:
3592:
3590:
3587:
3585:
3582:
3580:
3577:
3576:
3574:
3572:
3568:
3562:
3559:
3555:
3552:
3548:
3545:
3543:
3540:
3539:
3538:
3535:
3534:
3533:
3530:
3526:
3523:
3521:
3518:
3516:
3513:
3511:
3508:
3507:
3506:
3503:
3502:
3500:
3498:
3494:
3491:
3489:
3485:
3479:
3476:
3474:
3471:
3467:
3464:
3463:
3462:
3459:
3457:
3454:
3450:
3449:loss function
3447:
3446:
3445:
3442:
3438:
3435:
3433:
3430:
3428:
3425:
3424:
3423:
3420:
3418:
3415:
3413:
3410:
3406:
3403:
3401:
3398:
3396:
3390:
3387:
3386:
3385:
3382:
3378:
3375:
3373:
3370:
3368:
3365:
3364:
3363:
3360:
3356:
3353:
3351:
3348:
3347:
3346:
3343:
3339:
3336:
3335:
3334:
3331:
3327:
3324:
3323:
3322:
3319:
3317:
3314:
3312:
3309:
3307:
3304:
3303:
3301:
3299:
3295:
3291:
3287:
3282:
3278:
3264:
3261:
3259:
3256:
3254:
3251:
3249:
3246:
3245:
3243:
3241:
3237:
3231:
3228:
3226:
3223:
3221:
3218:
3217:
3215:
3211:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3171:
3169:
3167:
3163:
3157:
3154:
3152:
3151:Questionnaire
3149:
3147:
3144:
3140:
3137:
3135:
3132:
3131:
3130:
3127:
3126:
3124:
3122:
3118:
3112:
3109:
3107:
3104:
3102:
3099:
3097:
3094:
3092:
3089:
3087:
3084:
3082:
3079:
3077:
3074:
3073:
3071:
3069:
3065:
3061:
3057:
3052:
3048:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2989:
2986:
2984:
2981:
2979:
2978:Control chart
2976:
2974:
2971:
2969:
2966:
2964:
2961:
2960:
2958:
2956:
2952:
2946:
2943:
2939:
2936:
2934:
2931:
2930:
2929:
2926:
2924:
2921:
2919:
2916:
2915:
2913:
2911:
2907:
2901:
2898:
2896:
2893:
2891:
2888:
2887:
2885:
2881:
2875:
2872:
2871:
2869:
2867:
2863:
2851:
2848:
2846:
2843:
2841:
2838:
2837:
2836:
2833:
2831:
2828:
2827:
2825:
2823:
2819:
2813:
2810:
2808:
2805:
2803:
2800:
2798:
2795:
2793:
2790:
2788:
2785:
2783:
2780:
2779:
2777:
2775:
2771:
2765:
2762:
2760:
2757:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
2728:
2725:
2723:
2720:
2718:
2715:
2713:
2710:
2708:
2705:
2704:
2703:
2700:
2699:
2697:
2695:
2691:
2688:
2686:
2682:
2678:
2674:
2669:
2665:
2659:
2656:
2654:
2651:
2650:
2647:
2643:
2636:
2631:
2629:
2624:
2622:
2617:
2616:
2613:
2604:
2599:
2596:(17): 34â43.
2595:
2591:
2590:
2585:
2581:
2577:
2573:
2569:
2565:
2561:
2560:
2555:
2551:
2547:
2545:0-471-02403-1
2541:
2536:
2535:
2528:
2525:
2524:0-387-94037-5
2521:
2517:
2513:
2510:
2508:
2507:0-8247-8253-4
2504:
2500:
2496:
2492:
2488:
2484:
2482:0-7923-2608-3
2478:
2474:
2470:
2465:
2462:
2461:0-387-94037-5
2458:
2454:
2450:
2446:
2445:Hoeffding, W.
2443:
2440:
2436:
2435:Fisher, R. A.
2433:
2431:
2430:0-412-12420-3
2427:
2423:
2419:
2415:
2411:
2407:
2405:90-6764-200-2
2401:
2397:
2393:
2389:
2388:
2376:
2373:
2369:
2365:
2362:
2356:
2347:
2338:
2330:
2326:
2322:
2320:0-8176-3572-6
2316:
2312:
2304:
2296:
2292:
2288:
2286:90-6764-200-2
2282:
2278:
2274:
2267:
2259:
2255:
2251:
2249:0-7923-2608-3
2245:
2241:
2237:
2229:
2220:
2211:
2202:
2198:
2188:
2185:
2184:
2178:
2176:
2172:
2155:
2130:
2126:
2122:
2119:
2116:
2111:
2107:
2098:
2094:
2085:
2064:
2060:
2056:
2051:
2047:
2043:
2038:
2034:
2027:
2018:
2004:
2001:
1998:
1990:
1987:, the sample
1968:
1965:
1962:
1953:
1950:
1947:
1937:
1933:
1928:
1918:
1908:
1901:
1896:
1892:
1885:
1882:
1876:
1868:
1865:
1862:
1858:
1837:
1828:
1814:
1811:
1808:
1788:
1785:
1782:
1775:with divisor
1759:
1756:
1753:
1746:
1740:
1730:
1720:
1713:
1708:
1704:
1697:
1694:
1688:
1680:
1676:
1668:
1652:
1648:
1642:
1632:
1628:
1624:
1619:
1615:
1608:
1600:
1596:
1592:
1587:
1583:
1576:
1567:
1553:
1550:
1547:
1520:
1516:
1512:
1507:
1503:
1492:
1489:
1486:
1482:
1472:
1469:
1466:
1460:
1453:
1449:
1446:
1438:
1434:
1430:
1427:
1424:
1419:
1415:
1406:
1402:
1374:
1370:
1366:
1361:
1357:
1348:
1340:
1336:
1332:
1327:
1323:
1316:
1307:
1293:
1289:
1280:
1276:
1272:
1269:
1266:
1261:
1257:
1250:
1245:
1235:
1228:
1222:
1214:
1210:
1189:
1186:
1180:
1174:
1160:
1158:
1153:
1149:
1145:
1140:
1136:
1132:
1128:
1125:of size
1124:
1119:
1117:
1113:
1109:
1104:
1102:
1099:, such as in
1098:
1094:
1089:
1087:
1069:
1065:
1055:
1053:
1035:
1032:
1029:
1025:
1002:
999:
996:
992:
960:
956:
951:
947:
944:
941:
934:
930:
925:
918:
911:
908:
905:
901:
897:
889:
885:
881:
878:
875:
870:
866:
858:
845:
842:
832:
827:
819:
815:
811:
808:
805:
800:
796:
787:
783:
775:
774:
773:
759:
728:
724:
719:
715:
712:
709:
702:
698:
693:
686:
679:
676:
673:
669:
665:
657:
653:
649:
646:
643:
638:
634:
626:
616:
613:
610:
602:
599:
596:
591:
588:
585:
581:
576:
571:
563:
559:
555:
552:
549:
544:
540:
531:
527:
519:
518:
517:
500:
497:
494:
491:
488:
485:
482:
459:
437:
434:
431:
427:
419:over the set
399:
395:
390:
386:
383:
380:
373:
369:
364:
357:
337:
329:
319:
315:
308:
303:
299:
278:
275:
272:
252:
233:
213:
193:
185:
175:
171:
164:
161:
141:
132:
124:
122:
118:
114:
113:Pranab K. Sen
110:
107:
102:
100:
99:random graphs
96:
92:
88:
78:
76:
72:
68:
64:
63:
57:
53:
49:
44:
42:
37:
33:
19:
4962:U-statistics
4923:
4911:
4892:
4885:
4797:Econometrics
4747: /
4730:Chemometrics
4707:Epidemiology
4700: /
4673:Applications
4515:ARIMA model
4462:Q-statistic
4411:Stationarity
4307:Multivariate
4250: /
4246: /
4244:Multivariate
4242: /
4182: /
4178: /
3952:Bayes factor
3851:Signed rank
3763:
3737:
3729:
3717:
3431:
3412:Completeness
3248:Cohort study
3146:Opinion poll
3081:Missing data
3068:Study design
3023:Scatter plot
2945:Scatter plot
2938:Spearman's Ï
2900:Grouped data
2593:
2587:
2563:
2557:
2554:Tukey, J. W.
2533:
2515:
2498:
2472:
2468:
2452:
2438:
2421:
2395:
2392:
2375:Banach space
2368:vector space
2361:exchangeable
2355:
2346:
2337:
2310:
2307:Page xii in
2303:
2276:
2273:
2266:
2239:
2235:
2232:Page 508 in
2228:
2219:
2210:
2201:
2019:
1991:defined for
1829:
1568:
1308:
1166:
1156:
1151:
1147:
1143:
1138:
1134:
1130:
1126:
1122:
1120:
1107:
1105:
1090:
1056:
1051:
983:
751:
133:
130:
111:
103:
84:
60:statistical
59:
55:
45:
35:
29:
4925:WikiProject
4840:Cartography
4802:Jurimetrics
4754:Reliability
4485:Time domain
4464:(LjungâBox)
4386:Time-series
4264:Categorical
4248:Time-series
4240:Categorical
4175:(Bernoulli)
4010:Correlation
3990:Correlation
3786:JarqueâBera
3758:Chi-squared
3520:M-estimator
3473:Asymptotics
3417:Sufficiency
3184:Interaction
3096:Replication
3076:Effect size
3033:Violin plot
3013:Radar chart
2993:Forest plot
2983:Correlogram
2933:Kendall's Ï
2473:-statistics
2240:-statistics
2187:V-statistic
1850:-statistic
36:U-statistic
18:U statistic
4941:Categories
4792:Demography
4510:ARMA model
4315:Regression
3892:(Friedman)
3853:(Wilcoxon)
3791:Normality
3781:Lilliefors
3728:Student's
3604:Resampling
3478:Robustness
3466:divergence
3456:Efficiency
3394:(monotone)
3389:Likelihood
3306:Population
3139:Stratified
3091:Population
2910:Dependence
2866:Count data
2797:Percentile
2774:Dispersion
2707:Arithmetic
2642:Statistics
2580:Halmos, P.
2512:Sen, P. K.
2469:Theory of
2385:References
2236:Theory of
2223:Sen (1992)
1830:The third
1052:increasing
984:where now
127:Definition
97:, such as
62:functional
4173:Logistic
3940:posterior
3866:Rank sum
3614:Jackknife
3609:Bootstrap
3427:Bootstrap
3362:Parameter
3311:Statistic
3106:Statistic
3018:Run chart
3003:Pie chart
2998:Histogram
2988:Fan chart
2963:Bar chart
2845:L-moments
2732:Geometric
2372:separable
2175:L-moments
2120:…
2002:≥
1966:−
1951:−
1912:¯
1902:−
1886:∑
1812:≥
1786:−
1757:−
1724:¯
1714:−
1698:∑
1625:−
1551:≥
1513:−
1483:∑
1470:−
1428:…
1367:−
1270:⋯
1239:¯
1106:Fisher's
945:…
898:∈
879:…
859:∑
809:…
713:…
666:∈
647:…
627:∑
614:−
600:−
582:∏
553:…
495:…
384:…
335:→
309::
276:≥
191:→
165::
4887:Category
4580:Survival
4457:Johansen
4180:Binomial
4135:Isotonic
3722:(normal)
3367:location
3174:Blocking
3129:Sampling
3008:QâQ plot
2973:Box plot
2955:Graphics
2850:Skewness
2840:Kurtosis
2812:Variance
2742:Heronian
2737:Harmonic
2582:(1946).
2181:See also
1989:skewness
1163:Examples
1112:polykays
1054:tuples.
4913:Commons
4860:Kriging
4745:Process
4702:studies
4561:Wavelet
4394:General
3561:Plug-in
3355:L space
3134:Cluster
2835:Moments
2653:Outline
2491:1472486
2414:1419498
2329:1167198
2295:1419498
2258:1472486
2082:is the
1144:xφ
81:History
4782:Census
4372:Normal
4320:Manova
4140:Robust
3890:2-way
3882:1-way
3720:-test
3391:
2968:Biplot
2759:Median
2752:Lehmer
2694:Center
2542:
2522:
2505:
2489:
2479:
2459:
2428:
2412:
2402:
2327:
2317:
2293:
2283:
2256:
2246:
2084:median
1148:ƒ
1135:ƒ
1123:φ
54:of an
4406:Trend
3935:prior
3877:anova
3766:-test
3740:-test
3732:-test
3639:Power
3584:Pivot
3377:shape
3372:scale
2822:Shape
2802:Range
2747:Heinz
2722:Cubic
2658:Index
2193:Notes
206:be a
4639:Test
3839:Sign
3691:Wald
2764:Mode
2702:Mean
2540:ISBN
2520:ISBN
2503:ISBN
2477:ISBN
2457:ISBN
2426:ISBN
2400:ISBN
2315:ISBN
2281:ISBN
2244:ISBN
1490:>
134:Let
34:, a
3819:BIC
3814:AIC
2598:doi
2568:doi
1569:If
1309:If
1159:).
1050:of
452:of
30:In
4943::
2592:.
2586:.
2564:45
2562:.
2487:MR
2485:.
2410:MR
2408:.
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2325:MR
2323:.
2291:MR
2289:.
2254:MR
2252:.
2177:.
1827:.
1566:.
1088:.
101:.
43:.
3764:G
3738:F
3730:t
3718:Z
3437:V
3432:U
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2627:t
2620:v
2606:.
2600::
2594:1
2574:.
2570::
2548:.
2526:.
2493:.
2471:U
2463:)
2416:.
2394:U
2370:(
2331:.
2297:.
2275:U
2260:.
2238:U
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2117:,
2112:1
2108:x
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2099:n
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2070:)
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2005:3
1999:n
1975:)
1972:)
1969:2
1963:n
1960:(
1957:)
1954:1
1948:n
1945:(
1942:(
1938:/
1934:n
1929:3
1925:)
1919:n
1909:x
1897:i
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1889:(
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1880:)
1877:x
1874:(
1869:n
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1863:3
1859:k
1838:k
1815:2
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1692:)
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1606:)
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1476:)
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1328:1
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1281:n
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1215:n
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1181:x
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1175:f
1157:x
1155:(
1152:N
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1139:n
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