CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2009, 25(2) 171-184 DOI:      ISSN: 1001-4268 CN: 31-1256

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Keywords
Semiparametric model
MCNR
mixed model
generalized linear model
asympotitic properties.
Authors
Zhang Hao
Zhu Zhongyi
PubMed
Article by
Article by

Asymptotic Properties of Estimation in GeneralizedPartial Linear Mixed Models

Zhang Hao, Zhu Zhongyi

Department of Statistics, East China Normal University;Department of Statistics, Fudan University

Abstract��

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.

Keywords�� Semiparametric model   MCNR   mixed model   generalized linear model   asympotitic properties.  
Received 1900-01-01 Revised 1900-01-01 Online:  
DOI:
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Corresponding Authors: Zhang Hao
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