Open Access
Translator Disclaimer
September, 1974 An Unbalanced Jackknife
Rupert G. Miller Jr
Ann. Statist. 2(5): 880-891 (September, 1974). DOI: 10.1214/aos/1176342811

Abstract

It is proved that the jackknife estimate $\tilde{\theta} = n\hat{\theta} - (n - 1)(\sum \hat{\theta}_{-i}/n)$ of a function $\theta = f(\beta)$ of the regression parameters in a general linear model $\mathbf{Y} = \mathbf{X\beta} + \mathbf{e}$ is asymptotically normally distributed under conditions that do not require $\mathbf{e}$ to be normally distributed. The jackknife is applied by deleting in succession each row of the $\mathbf{X}$ matrix and $\mathbf{Y}$ vector in order to compute $\hat{\mathbf{\beta}}_{-i}$, which is the least squares estimate with the $i$th row deleted, and $\hat{\theta}_{-i} = f(\hat\mathbf{\beta}_{-i})$. The standard error of the pseudo-values $\tilde{\theta}_i = n\hat{\theta} - (n - 1)\hat{\theta}_{-i}$ is a consistent estimate of the asymptotic standard deviation of $\tilde{\theta}$ under similar conditions. Generalizations and applications are discussed.

Citation

Download Citation

Rupert G. Miller Jr. "An Unbalanced Jackknife." Ann. Statist. 2 (5) 880 - 891, September, 1974. https://doi.org/10.1214/aos/1176342811

Information

Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0289.62042
MathSciNet: MR356353
Digital Object Identifier: 10.1214/aos/1176342811

Subjects:
Primary: 62G05
Secondary: 62E20

Keywords: 15 , 35 , asymptotic normality , General linear model , jackknife , multiple regression , Pseudo-value

Rights: Copyright © 1974 Institute of Mathematical Statistics

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.2 • No. 5 • September, 1974
Back to Top