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Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data

Author

Listed:
  • Jia Chen
  • Degui Li
  • Hua Liang
  • Suojin Wang

Abstract

In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on the combination of the local linear smoothing and generalized estimation equations (GEE) is introduced to estimate the two parameter vectors as well as the unknown link function. Under some mild conditions, we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios, from which we find that the convergence rates and asymptotic variances of the proposed estimators for sparse longitudinal data would be substantially different from those for dense longitudinal data. We also discuss the estimation of the covariance (or weight) matrices involved in the semiparametric GEE method. Furthermore, we provide some numerical studies to illustrate our methodology and theory.

Suggested Citation

  • Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:14/26
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    References listed on IDEAS

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    Cited by:

    1. Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, vol. 4(1), pages 1-14, December.
    2. Brajendra C. Sutradhar, 2018. "Semi-parametric Dynamic Models for Longitudinal Ordinal Categorical Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 80-109, February.

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    More about this item

    Keywords

    GEE; local linear smoothing; longitudinal data; semiparametric estimation; single-index models.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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