The Annals of Statistics

Efficiency and Robustness in Resampling

Regina Y. Liu and Kesar Singh

Full-text: Open access

Abstract

It is known that the standard delete-1 jackknife and the classical bootstrap are in general equally efficient for estimating the mean-square-error of a statistic in the i.i.d. setting. However, this equivalence no longer holds in the linear regression model. It turns out that the bootstrap is more efficient when error variables are homogeneous and the jackknife is more robust when they are heterogeneous. In fact, we can divide all the commonly used resampling procedures for linear regression models into two types: the E-type (the efficient ones like the bootstrap) and the R-type (the robust ones like the jackknife). Thus the theory presented here provides a unified view of all the known resampling procedures in linear regression.

Article information

Source
Ann. Statist., Volume 20, Number 1 (1992), 370-384.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348527

Digital Object Identifier
doi:10.1214/aos/1176348527

Mathematical Reviews number (MathSciNet)
MR1150349

Zentralblatt MATH identifier
0755.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G15: Tolerance and confidence regions

Keywords
Asymptotic variance bootstrap procedures jackknife procedures resampling asymptotic relative efficiency E-type R-type

Citation

Liu, Regina Y.; Singh, Kesar. Efficiency and Robustness in Resampling. Ann. Statist. 20 (1992), no. 1, 370--384. doi:10.1214/aos/1176348527. https://projecteuclid.org/euclid.aos/1176348527


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