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Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model

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  • Lai, Peng
  • Wang, Qihua
  • Zhou, Xiao-Hua

Abstract

An efficient estimating equations procedure is developed for performing variable selection and defining semiparametric efficient estimates simultaneously for the heteroscedastic partially linear single-index model. The estimating equations are proposed based on the smooth threshold estimating equations by using the efficient score function of partially linear single-index models. And this estimating equations procedure can be used to perform variable selection without solving any convex optimization problems, and automatically eliminate nonsignificant variables by setting their coefficients as zero. The resulting estimators enjoy the oracle property and are semiparametrically efficient. The finite sample properties of the proposed estimators are illustrated by some simulation examples, as well as a real data application.

Suggested Citation

  • Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:241-256
    DOI: 10.1016/j.csda.2013.09.012
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    References listed on IDEAS

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    Cited by:

    1. Peng Lai & Fangjian Wang & Tingyu Zhu & Qingzhao Zhang, 2021. "Model identification and selection for single-index varying-coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 457-480, June.
    2. Peirong Xu & Jun Zhang & Xingfang Huang & Tao Wang, 2016. "Efficient estimation for marginal generalized partially linear single-index models with longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-431, September.
    3. Lai, Peng & Zhang, Qingzhao & Lian, Heng & Wang, Qihua, 2016. "Efficient estimation for the heteroscedastic single-index varying coefficient models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 84-93.

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