286:(i.e., truncate the sample by 38% at each end) produces an estimate for the population location parameter that is more efficient than using either the sample median or the full sample mean. However, due to the fat tails of the Cauchy distribution, the efficiency of the estimator decreases as more of the sample gets used in the estimate. Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a
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would mean discarding 1 point from each end (equivalent to the 10% trimmed mean). If interpolating, one would instead compute the 10% trimmed mean (discarding 1 point from each end) and the 20% trimmed mean (discarding 2 points from each end), and then interpolating, in this case averaging these two values. Similarly, if interpolating the 12% trimmed mean, one would take the
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For most statistical applications, 5 to 25 percent of the ends are discarded. For example, given a set of 8 points, trimming by 12.5% would discard the minimum and maximum value in the sample: the smallest and largest values, and would compute the mean of the remaining 6 points. The 25% trimmed mean
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Once the quotes are compiled, LIBOR uses a trimmed mean process, in which the highest and lowest values are thrown out and the remaining values are averaged. This is sometimes called an "Olympic average" from its use in the
Olympics to eliminate the impact of a biased judge on an athlete's final
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When the percentage of points to discard does not yield a whole number, the trimmed mean may be defined by interpolation, generally linear interpolation, between the nearest whole numbers. For example, if you need to calculate the 15% trimmed mean of a sample containing 10 entries, strictly this
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at the high and low end, and typically discarding an equal amount of both. This number of points to be discarded is usually given as a percentage of the total number of points, but may also be given as a fixed number of points.
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estimator, nor are any as asymptotically efficient as the maximum likelihood estimator; however, the maximum likelihood estimate is more difficult to compute, leaving the truncated mean as a useful alternative.
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The 5th percentile (−6.75) lies between −40 and −5, while the 95th percentile (148.6) lies between 101 and 1053 (values shown in bold). Then, a 5% trimmed mean would result in the following:
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than the mean but will still give a reasonable estimate of central tendency or mean for many statistical models. In this regard it is referred to as a
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as a trimmed mean: given 18 responses, the top 4 and bottom 4 are discarded, and the remaining 10 are averaged (yielding trim factor of 4/18 ≈ 22%).
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534:(1978). "Maximum Likelihood Estimates of the Parameters of the Cauchy Distribution for Samples of Size 3 and 4".
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Rothenberg, Thomas J.; Fisher, Franklin, M.; Tilanus, C.B. (1964). "A note on estimation from a cauchy sample".
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Bloch, Daniel (1966). "A note on the estimation of the location parameters of the Cauchy distribution".
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based on the truncated mean, which is called Yuen's t-test, which also has several implementations in
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Yuen, K.K. (1974) The two-sample trimmed t for unequal population variances. Biometrika, 61, 165-170.
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Wilcox, R.R. (2005). Introduction to robust estimation and hypothesis testing. Academic Press.
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One situation in which it can be advantageous to use a truncated mean is when estimating the
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Arulmozhi, G.; Statistics For
Management, 2nd Edition, Tata McGraw-Hill Education, 2009, p.
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discard the lowest and the highest scores; calculate the mean value of the remaining scores
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The median can be regarded as a fully truncated mean and is most robust. As with other
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The truncated mean is a useful estimator because it is less sensitive to
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for mixed distributions and heavy-tailed distribution (like the
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that are evaluated by a panel of judges is a truncated mean:
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Discarding only the maximum and minimum is known as the
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This example can be compared with the one using the
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588:"WRS2: A Collection of Robust Statistical Methods"
617:"Removing Judges' Bias Is Olympic-Size Challenge"
230:), due to its use in Olympic events, such as the
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536:Journal of the American Statistical Association
498:Journal of the American Statistical Association
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602:"DescTools: Tools for Descriptive Statistics"
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621:The Wall Street Journal
642:"bbalibor: The Basics"
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199:it is also known as a
430:"Lessons from LIBOR"
54:improve this article
604:. 9 September 2021.
532:Ferguson, Thomas S.
280:normal distribution
276:Cauchy distribution
195:In some regions of
185:Cauchy distribution
392:Interquartile mean
288:maximum likelihood
272:location parameter
232:ISU Judging System
177:trimmed estimators
170:interquartile mean
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295:Statistical tests
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52:Please help
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626:7 September
377:procedure.
375:Winsorising
191:Terminology
142:statistical
656:Categories
403:References
332:calculated
255:Advantages
181:efficiency
80:newspapers
341:{92, 19,
110:July 2010
381:See also
311:Examples
261:outliers
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161:sample
153:median
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552:JSTOR
514:JSTOR
328:Libor
274:of a
140:is a
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628:2014
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347:1053
326:The
151:and
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