Asymptotic results with estimating equations for time-evolving clustered data

TL;DR

This paper develops asymptotic theory for estimators based on estimating functions in time-evolving clustered data, allowing for complex dependencies and varying distributions, with practical applications demonstrated.

Contribution

It introduces a quasi-likelihood framework for constructing asymptotically optimal estimating equations in complex, evolving clustered data models.

Findings

Establishes strong consistency and asymptotic normality of estimators.

Identifies asymptotically optimal estimating functions.

Demonstrates effectiveness through simulations and real data analysis.

Abstract

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data, with distributions belonging to the exponential family, and which may also vary in terms of other component series. Within a quasi-likelihood approach, we construct estimating equations, which accommodate different forms of dependency among the components of the response vector and establish multivariate extensions of results on linear and generalized linear models, with stochastic covariates. Furthermore, we characterize estimating functions which are asymptotically optimal, in that they lead to confidence regions for the regression parameters which are of minimum size, asymptotically. Results from a simulation study and an application to a real dataset are included.