Asymptotic Inferences in a Doubly-Semi-Parametric Linear Longitudinal Mixed Model
Tóm tắt
Warriyar and Sutradhar (Brazilian J. Probab. Stat., 28, 561–586, 2014) studied a semi-parametric linear model in a longitudinal setup with Gaussian errors, where the main regression parameters were estimated using an efficient GQL (generalized quasi-likelihood) estimation approach, and the efficiency properties of the estimators were examined through a simulation study. In this paper we provide a generalization of their linear semi-parametric regression model to a wider setup where the error distributions are relaxed and errors are assumed to follow a four-moments based semi-parametric structure leading to a doubly semi-parametric model. On top of regression parameters and nonparametric function estimation, this doubly semi-parametric nature of the model makes the four-moments based variance and correlation parameters estimation quite challenging. We resolve this computational issue analytically by developing exact formulas for all necessary higher order moments. As the longitudinal studies involve large number of independent individuals providing repeated responses, we study the asymptotic properties of the estimators and make sure that the estimators including the estimator of nonparametric function are consistent.
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