## The Annals of Statistics

### Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis

C. F. J. Wu

#### Abstract

Motivated by a representation for the least squares estimator, we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time. They are unbiased for homoscedastic errors and a special case, the delete-one jackknife, is almost unbiased for heteroscedastic errors. The method is extended to cover nonlinear parameters, regression $M$-estimators, nonlinear regression and generalized linear models. Interval estimators can be constructed from the jackknife histogram. Three bootstrap methods are considered. Two are shown to give biased variance estimators and one does not have the bias-robustness property enjoyed by the weighted delete-one jackknife. A general method for resampling residuals is proposed. It gives variance estimators that are bias-robust. Several bias-reducing estimators are proposed. Some simulation results are reported.

#### Article information

Source
Ann. Statist. Volume 14, Number 4 (1986), 1261-1295.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350142

JSTOR

Digital Object Identifier
doi:10.1214/aos/1176350142

Mathematical Reviews number (MathSciNet)
MR868303

Zentralblatt MATH identifier
0618.62072

Subjects
Primary: 62J05: Linear regression
Secondary: 62J02: General nonlinear regression 62G05: Estimation

#### Citation

Wu, C. F. J. Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis. The Annals of Statistics 14 (1986), no. 4, 1261--1295. doi:10.1214/aos/1176350142. http://projecteuclid.org/euclid.aos/1176350142.