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A robust and efficient estimation and variable selection method for partially linear single-index models

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  • Yang, Hu
  • Yang, Jing

Abstract

In this paper, a new robust and efficient estimation approach based on local modal regression is proposed for partially linear single-index models, of which the univariate nonparametric link function is approximated by local polynomial regression. The asymptotic normality of proposed estimators for both the parametric and nonparametric parts are established. We show that the resulting estimator is more efficient than the ordinary least-square-based estimation in the case of outliers or heavy-tail error distribution, and as asymptotically efficient as the least square estimator when there are no outliers and the error is normal distribution. To achieve sparsity when there exist irrelevant variables in the model, a variable selection procedure based on SCAD penalty is developed to select significant parametric covariates and is shown to possess oracle property under some regularity conditions. We also propose a practical modified EM algorithm for the new method. Some Monte Carlo simulations and a real data set are conducted to illustrate the finite sample performance of the proposed estimators.

Suggested Citation

  • Yang, Hu & Yang, Jing, 2014. "A robust and efficient estimation and variable selection method for partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 227-242.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:227-242
    DOI: 10.1016/j.jmva.2014.04.024
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    Cited by:

    1. Yunquan Song & Yaqi Liu & Hang Su, 2022. "Robust Variable Selection for Single-Index Varying-Coefficient Model with Missing Data in Covariates," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    2. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    3. Yang, Jing & Yang, Hu, 2016. "A robust penalized estimation for identification in semiparametric additive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 268-277.
    4. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Qingyang Liu & Xianzheng Huang & Haiming Zhou, 2024. "The Flexible Gumbel Distribution: A New Model for Inference about the Mode," Stats, MDPI, vol. 7(1), pages 1-16, March.

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