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arXiv · 2303.16639

On local likelihood asymptotics for Gaussian mixed-effects model with system noise

Takumi Imamura·Hiroki Masuda·Hayato Tajima
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Abstract

The Gaussian mixed-effects model driven by a stationary integrated Ornstein-Uhlenbeck process has been used for analyzing longitudinal data having an explicit and simple serial-correlation structure in each individual. However, the theoretical aspect of its asymptotic inference is yet to be elucidated. We prove the local asymptotics for the associated log-likelihood function, which in particular guarantees the asymptotic optimality of the suitably chosen maximum-likelihood estimator. We illustrate the obtained asymptotic normality result through some simulations for both balanced and unbalanced datasets.

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Takumi Imamura, Hiroki Masuda, Hayato Tajima. 2023-03-29. On local likelihood asymptotics for Gaussian mixed-effects model with system noise. https://arxiv.org/abs/2303.16639

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