General Unbiased Estimating Equations for Variance Components in Linear Mixed Models

TL;DR

This paper develops a comprehensive framework for unbiased estimation of variance components in linear mixed models using general estimating equations, applicable without assuming normality, and provides theoretical and numerical validation.

Contribution

It introduces a unified approach for variance component estimation via unbiased estimating equations, extending existing methods and deriving new asymptotic properties without normality assumptions.

Findings

Derived asymptotic covariance matrices and biases for estimators.

Identified a class of second-order unbiased estimators.

Numerical studies confirm the effectiveness of the proposed methods.

Abstract

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator. We derive the asymptotic covariance matrices and second-order biases under general estimating equations without assuming the normality of the underlying distributions and identify a class of second-order unbiased estimators of variance components. It is also shown that the asymptotic covariance matrices and second-order biases do not depend on whether the regression coefficients are estimated by the generalized or ordinary least squares methods. We carry out numerical studies to check the performance of the proposed method based on typical linear mixed models.