Breakdown Theory for Bootstrap Quantiles

A general formula for computing the breakdown point (in robustness) for the tth bootstrap quantile of a statistic Tnis obtained. The answer depends on t and the breakdown point of Tn. Since the bootstrap quantiles are vital ingredients of bootstrap confidence intervals, the theory has implications p...

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Bibliographic Details
Published in:	The Annals of statistics Vol. 26; no. 5; pp. 1719 - 1732
Main Author:	Singh, Kesar
Format:	Journal Article
Language:	English
Published:	Hayward, CA Institute of Mathematical Statistics 01-10-1998 The Institute of Mathematical Statistics
Subjects:	62G09 62G15 Bootstrap Bootstrap resampling breakdown in robustness Estimators Exact sciences and technology Integers L and M estimators Logical theorems Mathematics Nonparametric inference Outliers Population density Probability and statistics Quantiles Reasoning Resampling and Classification Sampling distributions Sciences and techniques of general use Statistical theories Statistics Winsorization L estimation Estimator robustness Bootstrap Non parametric estimation Statistical estimation Breakdown point Quantile M estimation Confidence interval
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Summary:	A general formula for computing the breakdown point (in robustness) for the tth bootstrap quantile of a statistic Tnis obtained. The answer depends on t and the breakdown point of Tn. Since the bootstrap quantiles are vital ingredients of bootstrap confidence intervals, the theory has implications pertaining to robustness of bootstrap confidence intervals. For certain L and M estimators, a robustification of bootstrap is suggested via the notion of Winsorization.
ISSN:	0090-5364 2168-8966
DOI:	10.1214/aos/1024691354