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February 2014 Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data
Guang Cheng, Lan Zhou, Jianhua Z. Huang
Bernoulli 20(1): 141-163 (February 2014). DOI: 10.3150/12-BEJ479

Abstract

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based on a spline approximation of the nonparametric part of the model and the generalized estimating equations (GEE). Although the model in consideration is natural and useful in many practical applications, the literature on this model is very limited because of challenges in dealing with dependent data for nonparametric additive models. We show that the proposed estimators are consistent and asymptotically normal even if the covariance structure is misspecified. An explicit consistent estimate of the asymptotic variance is also provided. Moreover, we derive the semiparametric efficiency score and information bound under general moment conditions. By showing that our estimators achieve the semiparametric information bound, we effectively establish their efficiency in a stronger sense than what is typically considered for GEE. The derivation of our asymptotic results relies heavily on the empirical processes tools that we develop for the longitudinal/clustered data. Numerical results are used to illustrate the finite sample performance of the proposed estimators.

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Guang Cheng. Lan Zhou. Jianhua Z. Huang. "Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data." Bernoulli 20 (1) 141 - 163, February 2014. https://doi.org/10.3150/12-BEJ479

Information

Published: February 2014
First available in Project Euclid: 22 January 2014

zbMATH: 06282545
MathSciNet: MR3160576
Digital Object Identifier: 10.3150/12-BEJ479

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 1 • February 2014
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