The Annals of Statistics

Bahadur Representations for Uniform Resampling and Importance Resampling, with Applications to Asymptotic Relative Efficiency

Peter Hall

Full-text: Open access

Abstract

We derive Bahadur-type representations for quantile estimates obtained from two different types of nonparametric bootstrap resampling--the commonly used uniform resampling method, where each sample value is drawn with the same probability, and importance resampling, where different sample values are assigned different resampling weights. These results are applied to obtain the relative efficiency of uniform resampling and importance resampling and to derive exact convergence rates, both weakly and strongly, for either type of resampling.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 1062-1072.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348138

Digital Object Identifier
doi:10.1214/aos/1176348138

Mathematical Reviews number (MathSciNet)
MR1105862

Zentralblatt MATH identifier
0725.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Bahadur representation bootstrap efficiency importance sampling quantile strong approximation uniform resampling

Citation

Hall, Peter. Bahadur Representations for Uniform Resampling and Importance Resampling, with Applications to Asymptotic Relative Efficiency. Ann. Statist. 19 (1991), no. 2, 1062--1072. doi:10.1214/aos/1176348138. https://projecteuclid.org/euclid.aos/1176348138


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