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Dispersion Parameter Extension of Precise Generalized Linear Mixed Model Asymptotics
arXiv - MATH - Statistics Theory Pub Date : 2022-08-10 , DOI: arxiv-2208.05301 Aishwarya Bhaskaran, Matt P. Wand
arXiv - MATH - Statistics Theory Pub Date : 2022-08-10 , DOI: arxiv-2208.05301 Aishwarya Bhaskaran, Matt P. Wand
We extend a recently established asymptotic normality theorem for generalized
linear mixed models to include the dispersion parameter. The new results show
that the maximum likelihood estimators of all model parameters have
asymptotically normal distributions with asymptotic mutual independence between
fixed effects, random effects covariance and dispersion parameters. The
dispersion parameter maximum likelihood estimator has a particularly simple
asymptotic distribution which enables straightforward valid likelihood-based
inference.
中文翻译:
精确广义线性混合模型渐近的色散参数扩展
我们为广义线性混合模型扩展了最近建立的渐近正态性定理,以包括色散参数。新结果表明,所有模型参数的最大似然估计量具有渐近正态分布,固定效应、随机效应协方差和离散参数之间具有渐近相互独立性。色散参数最大似然估计器具有特别简单的渐近分布,可实现直接有效的基于似然的推断。
更新日期:2022-08-11
中文翻译:
精确广义线性混合模型渐近的色散参数扩展
我们为广义线性混合模型扩展了最近建立的渐近正态性定理,以包括色散参数。新结果表明,所有模型参数的最大似然估计量具有渐近正态分布,固定效应、随机效应协方差和离散参数之间具有渐近相互独立性。色散参数最大似然估计器具有特别简单的渐近分布,可实现直接有效的基于似然的推断。