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Parameter estimation for a generalized semiparametric model with repeated measurements

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Abstract

In this paper, we propose a flexible generalized semiparametric model for repeated measurements by combining generalized partially linear single-index models with varying coefficient models. The proposed model is a useful analytic tool to explore dynamic patterns which naturally exist in longitudinal data and also study possible nonlinear relationships between the response and covariates. We then employ the quadratic inference function and develop an estimation procedure to estimate unknown regression parameters and nonparametric functions. To select variables and estimate parameters simultaneously, we further obtain penalized estimators. Moreover, we establish theoretical properties of the parametric and nonparametric estimators. Both simulations and an empirical example are presented to illustrate the use of the proposed model.

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Acknowledgments

The authors thank the Editor, the Associate and two anonymous referees for their helpful comments that led to significant improvements in the article.

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Authors and Affiliations

  1. Department of Statistics, University of California-Riverside, Riverside, CA, 92521, USA

    Shujie Ma & Zijian Huang

  2. Graduate School of Management, University of California-Davis, Davis, CA, 95616, USA

    Chih-Ling Tsai

Authors
  1. Shujie Ma
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  2. Zijian Huang
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  3. Chih-Ling Tsai
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Corresponding author

Correspondence to Shujie Ma.

Additional information

S. Ma’s research was partially supported by NSF Grant DMS 1306972.

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Ma, S., Huang, Z. & Tsai, CL. Parameter estimation for a generalized semiparametric model with repeated measurements. Ann Inst Stat Math 68, 725–764 (2016). https://doi.org/10.1007/s10463-015-0513-1

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  • DOI: https://doi.org/10.1007/s10463-015-0513-1

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