The Annals of Statistics

Asymptotics for generalized estimating equations with large cluster sizes

Minge Xie and Yaning Yang

Full-text: Open access

Abstract

Generalized estimating equations are used in regression analysis of longitudinal data, where observations on each subject are correlated. Statistical analysis using such methods is based on the asymptotic properties of regression parameter estimators. This paper presents asymptotic results when either the number of independent subjects or the cluster sizes (the number of observations on each subject) or both go to infinity. A set of (information matrix based) general conditions is developed, which leads to the weak and strong consistency as well as the asymptotic normality of the estimators. Most of the results are parallel to the elegant work of Fahrmeir and Kaufmann on maximum likelihood estimators related to the generalized linear models. The conditions for weak consistency and asymptotic normality are verified for several examples of general interest.

Article information

Source
Ann. Statist., Volume 31, Number 1 (2003), 310-347.

Dates
First available in Project Euclid: 26 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1046294467

Digital Object Identifier
doi:10.1214/aos/1046294467

Mathematical Reviews number (MathSciNet)
MR1962509

Zentralblatt MATH identifier
1018.62019

Subjects
Primary: 62F12: Asymptotic properties of estimators 62J12: Generalized linear models

Keywords
Generalized estimation equations (GEE) longitudinal data cluster correlated observations infinite cluster sizes

Citation

Xie, Minge; Yang, Yaning. Asymptotics for generalized estimating equations with large cluster sizes. Ann. Statist. 31 (2003), no. 1, 310--347. doi:10.1214/aos/1046294467. https://projecteuclid.org/euclid.aos/1046294467


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  • HILL CENTER, BUSCH CAMPUS
  • PISCATAWAY, NEW JERSEY 08854 E-MAIL: mxie@stat.rutgers.edu LABORATORY OF STATISTICAL GENETICS ROCKEFELLER UNIVERSITY
  • NEW YORK, NEW YORK 10021