The bootstrap: Some large sample theory and connections with robustness

William C. Parr

Statistics & Probability Letters, 1985, vol. 3, issue 2, 97-100

Abstract: The bootstrap, discussed by Efron (1979, 1981), is a powerful tool for the nonparametric estimation of sampling distributions and asymptotic standard errors. We demonstrate consistency of the bootstrap distribution estimates for a general class of robust differentiable statistical functionals. Our conditions for consistency of the bootstrap are variants of previously considered criteria for robustness of the associated statistics. A general example shows that, for almost any location statistic, consistency of the bootstrap variance estimator requires a tail condition on the distribution from which samples are taken. A modification of Efron's estimator of standard error is shown to circumvent this problem.

Keywords: bootstrap; continuity; differentiable; statistical; functionals; Fréchet; differentiability; robustness; strong; laws; variance; estimation (search for similar items in EconPapers)
Date: 1985
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Citations: View citations in EconPapers (8)

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