The Annals of Statistics

On Berry-Esseen Rates for Jackknife Estimators

K. F. Cheng

Full-text: Open access

Abstract

Consider an ordinary estimation problem for an unknown parameter $\theta$. Let the estimator $\theta^\ast_n$ be the jackknife of a function of a $U$-statistic. Under mild assumptions, we demonstrate that $\sup_t |P\lbrack n^{1/2}(\theta^\ast_n - \theta)/S^\ast_n \leq t \rbrack - \Phi (t)| = O(n^{-p/2(p+1)})$, where $S^{\ast 2}_n$ is a jackknife estimator of the asymptotic variance of $n^{1/2}\theta^\ast_n, \Phi (t)$ is the standard normal distribution and $p$ is some positive number.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 694-696.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345477

Digital Object Identifier
doi:10.1214/aos/1176345477

Mathematical Reviews number (MathSciNet)
MR615449

Zentralblatt MATH identifier
0477.62026

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 62G05: Estimation

Keywords
Jackknife $U$-statistic Berry-Esseen rates

Citation

Cheng, K. F. On Berry-Esseen Rates for Jackknife Estimators. Ann. Statist. 9 (1981), no. 3, 694--696. doi:10.1214/aos/1176345477. https://projecteuclid.org/euclid.aos/1176345477


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