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

2024/12/01 by Imamura, Takumi, Masuda, Hiroki
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2412.00796

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.

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