Gaussian quasi-likelihood analysis for non-Gaussian linear mixed-effects model with system noise
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917085066559488 |
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| author | Imamura, Takumi Masuda, Hiroki |
| author_facet | Imamura, Takumi Masuda, Hiroki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gaussian quasi-likelihood analysis for non-Gaussian linear mixed-effects model with system noise Imamura, Takumi Masuda, Hiroki Statistics Theory 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. |
| title | Gaussian quasi-likelihood analysis for non-Gaussian linear mixed-effects model with system noise |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2412.00796 |