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Efficient estimation for marginal generalized partially linear single-index models with longitudinal data

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Abstract

We consider marginal generalized partially linear single-index models for longitudinal data. A profile generalized estimating equations (GEE)-based approach is proposed to estimate unknown regression parameters. Within a wide range of bandwidths for estimating the nonparametric function, our profile GEE estimator is consistent and asymptotically normal even if the covariance structure is misspecified. Moreover, if the covariance structure is correctly specified, the semiparametric efficiency can be achieved under heteroscedasticity and without distributional assumptions on the covariates. Simulation studies are conducted to evaluate the finite sample performance of the proposed procedure. The proposed methodology is further illustrated through a data analysis.

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Acknowledgments

The authors thank the editor, the associate editor and two anonymous referees for their many helpful comments that have resulted in significant improvements in the article. Peirong Xu was supported by the Natural Science Foundation of Jiangsu Province, China (No. BK20140617) and the National Natural Science Foundation of China (NSFC) Grant No. 11501099. Jun Zhang was supported by the National Natural Science Foundation of China (NSFC) Grant No. 11401391 and the Project of Department of Education of Guangdong Province of China, Grant No. 2014KTSCX112. Xingfang Huang was supported by the National Natural Science Foundation of China (NSFC) Grant No. 11401094 and the Humanities and Social Science Foundation of Ministry of Education of China (13YJC910006).

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, China

    Peirong Xu & Xingfang Huang

  2. Shen Zhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Institute of Statistical Sciences, College of Mathematics and Statistics, Shenzhen University, Shenzhen, China

    Jun Zhang

  3. Department of Biostatistics, Yale School of Public Health, Yale University, New Haven, USA

    Tao Wang

Authors
  1. Peirong Xu
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  2. Jun Zhang
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  3. Xingfang Huang
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  4. Tao Wang
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Correspondence to Peirong Xu.

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Xu, P., Zhang, J., Huang, X. et al. Efficient estimation for marginal generalized partially linear single-index models with longitudinal data. TEST 25, 413–431 (2016). https://doi.org/10.1007/s11749-015-0462-2

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