Efficient estimation of moments in linear mixed models

TL;DR

This paper investigates the estimation of moments in linear mixed models without relying on distributional assumptions, focusing on the efficiency of estimators derived from multiple estimating equations.

Contribution

It provides a systematic study of moment estimators in linear mixed models, addressing the challenge of multiple estimating equations and their efficiency.

Findings

Analysis of multiple estimating equations for moments

Identification of conditions for estimator efficiency

Guidelines for practical implementation of moment estimators

Abstract

In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means. Generally, estimators may be obtained as solutions of estimating equations. It turns out that there may be several equations, each of them leading to consistent estimators, in which case finding the efficient estimator becomes a crucial problem. In this paper, we systematically study estimation of moments of the errors and random effects in linear mixed models.