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Variable selection for the partial linear single-index model

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Abstract

In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.

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Authors and Affiliations

  1. Department of Statistics, School of Management, Fudan University, Shanghai, 200433, China

    Wu Wang & Zhong-yi Zhu

Authors
  1. Wu Wang
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  2. Zhong-yi Zhu
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Correspondence to Zhong-yi Zhu.

Additional information

Supported by the National Natural Science Foundation of China (No. 11671096).

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Wang, W., Zhu, Zy. Variable selection for the partial linear single-index model. Acta Math. Appl. Sin. Engl. Ser. 33, 373–388 (2017). https://doi.org/10.1007/s10255-017-0666-1

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  • DOI: https://doi.org/10.1007/s10255-017-0666-1

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