Iterative estimating equations: Linear convergence and asymptotic properties

TL;DR

This paper introduces an iterative estimating equations method for longitudinal data analysis, demonstrating its exponential convergence, consistency, and efficiency, with applications to semiparametric models and practical validation through simulations and a medical case study.

Contribution

It presents a novel iterative estimating equations approach with proven convergence and efficiency for longitudinal data, applicable to complex semiparametric models.

Findings

Convergence probability approaches one with increasing sample size.

The estimator is consistent and asymptotically efficient.

Finite sample performance compares favorably with existing methods.

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.