The Annals of Statistics

Iterative estimating equations: Linear convergence and asymptotic properties

Jiming Jiang, Yihui Luan, and You-Gan Wang

Full-text: Open access

Abstract

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

Article information

Source
Ann. Statist., Volume 35, Number 5 (2007), 2233-2260.

Dates
First available in Project Euclid: 7 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1194461729

Digital Object Identifier
doi:10.1214/009053607000000208

Mathematical Reviews number (MathSciNet)
MR2363970

Zentralblatt MATH identifier
1126.62025

Subjects
Primary: 62J02: General nonlinear regression 65B99: None of the above, but in this section 62F12: Asymptotic properties of estimators

Keywords
Asymptotic efficiency consistency iterative algorithm linear convergence longitudinal data semiparametric regression

Citation

Jiang, Jiming; Luan, Yihui; Wang, You-Gan. Iterative estimating equations: Linear convergence and asymptotic properties. Ann. Statist. 35 (2007), no. 5, 2233--2260. doi:10.1214/009053607000000208. https://projecteuclid.org/euclid.aos/1194461729


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