Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations
type: Item
instance of: scholarly article
title: Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations
zbMATH Open document ID: 1383.62220
DOI: 10.1214/16-AOS1516
author: Peng Zhang
published in: The Annals of Statistics
publication date: 2017-12-22T00:00:00Z
review text: Modeling the expectation of a response variable \(V\) conditional on a set of covariates \(Z\) is a fundamental problem in statistical practice. When both response variable and covariates are observed from an independent and identically distributed (i.i.d) sample, estimation equations can be derived to estimate the unknown parameter \(\beta\) in the conditional expectation function. In many statistical applications, the response variable may not be observable for all subjects but a related and observable i.i.d. sample is available which can be used reasonably to estimate the unconditional mean of \(V\). It was suggested that jackknife pseudo-observations defined based on estimates of the unconditional mean of \(V\) can replace values of \(V\), which may not be observable, in the estimation equation to obtain consistent, asymptotically normal estimates of \(\beta\) with a variance that could be estimated consistently by the ordinary sandwich variance estimator. In a general setting and under some general conditions, this paper established the consistency and asymptotic normality of the estimates using recent functional analytic results. It is also found that the usual sandwich variance estimator is generally inconsistent, and a modification is proposed. Applications to several problems in survival analysis with censored responses are discussed in detail.
reviewed by: Dongsheng Tu
Mathematics Subject Classification ID: 62N02
Mathematics Subject Classification ID: 62J12
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 6821116
zbMATH Keywords: censoring
zbMATH Keywords: jackknife pseudo-values
zbMATH Keywords: functional differentiability
zbMATH Keywords: von Mises expansion
zbMATH Keywords: regression models
zbMATH Keywords: survival analysis
Wikidata QID: Q60646411
MaRDI profile type: Publication
full work available at URL: 16-aos1516
OpenAlex ID: W2766810949
description: scientific article; zbMATH DE number 6821116