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On using the jackknife to estimate quantile variance
Author(s) -
Martin Michael A.
Publication year - 1990
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315563
Subject(s) - jackknife resampling , studentized range , quantile , mathematics , statistics , estimator , statistic , variance (accounting) , delta method , sampling distribution , econometrics , standard error , accounting , business
We show that the jackknife technique fails badly when applied to the problem of estimating the variance of a sample quantile. When viewed as a point estimator, the jackknife estimator is known to be inconsistent. We show that the ratio of the jackknife variance estimate to the true variance has an asymptotic Weibull distribution with parameters 1 and 1/2. We also show that if the jackknife variance estimate is used to Studentize the sample quantile, the asymptotic distribution of the resulting Studentized statistic is markedly nonnormal, having infinite mean. This result is in stark contrast with that obtained in simpler problems, such as that of constructing confidence intervals for a mean, where the jackknife‐Studentized statistic has an asymptotic standard normal distribution.