## The Annals of Statistics

### Breakdown theory for bootstrap quantiles

Kesar Singh

#### Abstract

A general formula for computing the breakdown point in robustness for the $t$th bootstrap quantile of a statistic $T_n$ is obtained. The answer depends on $t$ and the breakdown point of $T_n$. 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.

#### Article information

Source
Ann. Statist., Volume 26, Number 5 (1998), 1719-1732.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691354

Digital Object Identifier
doi:10.1214/aos/1024691354

Mathematical Reviews number (MathSciNet)
MR1673275

Zentralblatt MATH identifier
0929.62053

Subjects
Primary: 62G09: Resampling methods 62G15

#### Citation

Singh, Kesar. Breakdown theory for bootstrap quantiles. Ann. Statist. 26 (1998), no. 5, 1719--1732. doi:10.1214/aos/1024691354. https://projecteuclid.org/euclid.aos/1024691354

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• PISCATAWAY, NEW JERSEY 08855 E-MAIL: kesar@stat.rutgers.edu