On the inconsistency of bootstrap distribution estimators

Hall, Peter;Härdle, Wolfgang;Simar, Léopold
(1993) Computational Statistics & Data Analysis — Vol. 16, n° 1, p. 11-18 (1993)

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  • Hall, PeterAustralian National University
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  • Härdle, WolfgangUCLouvain
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  • Simar, LéopoldUSL-B
    Author
Abstract
We show that bootstrap distribution estimators of a ranked parameter value are consistent if and only if there are no ties for the rank in question. When inconsistency occurs, the bootstrap distribution estimator does not even converge in probability. This asymptotic result has important implications for small to moderate sample sizes, where poor distribution estimators can result when there are no ties but there are two or more closely spaced parameter values competing to the same rank. Several ways of alleviating the problem of inconsistency are suggested. © 1993.
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Hall, P., Härdle, W., & Simar, L. (1993). On the inconsistency of bootstrap distribution estimators. Computational Statistics & Data Analysis, 16(1), 11-18. https://doi.org/10.1016/0167-9473(93)90241-K (Original work published 1993)