Jackknife, bootstrap and other resampling methods in regression analysis
type: Item
instance of: scholarly article
title: Jackknife, bootstrap and other resampling methods in regression analysis
zbMATH Open document ID: 0618.62072
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: Statistical inference based on data resampling has been mostly based on the assumption of independence and identical distribution, the i.i.d. case. The author maintains that resampling methods justifiable in the i.i.d. case may not work in more complex situations. These methods are studied in the context of regression models. New methods are proposed that take into account special features of regression data. A class of weighted jackknife variance estimators for the least squares estimator, which deletes a fixed number of observations at a time, is proposed. The proposed estimator is unbiased for homoscedastic errors. The special (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. Three bootstrap methods are considered. Two of them are biased variance estimators. A general method for resampling residuals is proposed. It gives variance estimators that are bias-robust.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62J02
zbMATH DE Number: 4003297
zbMATH Keywords: interval estimators
zbMATH Keywords: histogram
zbMATH Keywords: bias-reducing estimators
zbMATH Keywords: weighted delete-one jackknife variance estimators
zbMATH Keywords: variable jackknife
zbMATH Keywords: simulation results
zbMATH Keywords: jackknife percentile
zbMATH Keywords: Fieller's interval
zbMATH Keywords: resampling methods
zbMATH Keywords: weighted jackknife variance estimators
zbMATH Keywords: least squares estimator
zbMATH Keywords: homoscedastic errors
zbMATH Keywords: heteroscedastic errors
zbMATH Keywords: nonlinear parameters
zbMATH Keywords: regression M-estimators
zbMATH Keywords: generalized linear models
zbMATH Keywords: bootstrap methods
zbMATH Keywords: resampling residuals
zbMATH Keywords: bias-robust
author: C. F. Jeff Wu
reviewed by: Khursheed Alam
Wikidata QID: Q29030730
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350142
OpenAlex ID: W2104499761
DOI: 10.1214/AOS/1176350142
description: scientific article; zbMATH DE number 4003297