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A generalized semiparametric regression and its efficient estimation

Author

Listed:
  • Lu Lin
  • Lili Liu
  • Xia Cui
  • Kangning Wang

Abstract

We investigate a generalized semiparametric regression. Such a model can avoid the risk of wrongly choosing the base measure function. We propose a profile likelihood to efficiently estimate both parameter and nonparametric function. The main difference from the classical profile likelihood is that the profile likelihood proposed is a functional of the base measure function, instead of a function of a real variable. By making the most of the structure information of the semiparametric exponential family, we get an explicit expression of the estimator of the least favorable curve. It ensures that the new profile likelihood is computationally simple. Due to the use of the least favorable curve, the semiparametric efficiency is achieved successfully and the estimation bias is reduced significantly. Simulation studies can illustrate that our proposal is much better than the existing methodologies for most cases under study, and is robust to the different model conditions.

Suggested Citation

  • Lu Lin & Lili Liu & Xia Cui & Kangning Wang, 2021. "A generalized semiparametric regression and its efficient estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 1-24, March.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:1:p:1-24
    DOI: 10.1111/sjos.12430
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    References listed on IDEAS

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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    3. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    4. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    5. Lu Lin & Lixing Zhu & K. Yuen, 2005. "Profile empirical likelihood for parametric and semiparametric models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 485-505, September.
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