On Berry-Esseen Rates for Jackknife Estimators

Cheng, K. F.

Ann. Statist., Tome 9 (1981) no. 1, p. 694-696 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1981-05-14
Classification:  Jackknife,  $U$-statistic,  Berry-Esseen rates,  60B10,  62G05