Asymptotic Properties of Estimation in GeneralizedPartial Linear Mixed Models

Semiparametric models are useful in sychological, biological and medical application. Zhang (1998) used maximum penalized likelihood estimation (MPLE) to estimate both of the parametric and nonparametric parameters. Unfortunately, MPLE proposed by Zhang (1998) can only be applied to the Gaussian Models. In general, in order to estimate the parametric and nonparametric part in generalized partial linear mixed models, we choose to treat the random effects as the missing data and construct a Monte Carlo version of the EM algorithm. Based on the MCNR algorithm proposed by McCulloch (1997), we, in this paper, extend the algorithm to the eneralized partial linear mixed models (GPLMM) so that it may estimate both of the parameters and nonparameters simultaneously. In the new algorithm, we approximate the nonparametric function in GPLMM by P-spline and use GCV to choose the smoothing parameter. Meanwhile, we also give the proofs and the asymptotic properties of the estimators. Finally, in order to test the reliability of the method, the proposed algorithm is illustrated in the simulation analysis and one real data set.