Gaussian quasi-likelihood analysis for non-Gaussian linear mixed-effects model with system noise

TL;DR

This paper develops a Gaussian quasi-likelihood approach for non-Gaussian mixed-effects models with system noise, providing theoretical properties and a three-stage inference strategy, supported by numerical experiments.

Contribution

It introduces a novel quasi-likelihood method for non-Gaussian mixed-effects models with system noise and analyzes its asymptotic properties and inference strategies.

Findings

Asymptotic normality of the estimator

Tail-probability estimates established

Three-stage inference strategy shown to be first-order equivalent

Abstract

We consider statistical inference for a class of mixed-effects models with system noise described by a non-Gaussian integrated Ornstein-Uhlenbeck process. Under the asymptotics where the number of individuals goes to infinity with possibly unbalanced sampling frequency across individuals, we prove some theoretical properties of the Gaussian quasi-likelihood function, followed by the asymptotic normality and the tail-probability estimate of the associated estimator. In addition to the joint inference, we propose and investigate the three-stage inference strategy, revealing that they are first-order equivalent while quantitatively different in the second-order terms. Numerical experiments are given to illustrate the theoretical results.