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Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

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Abstract

This paper considers tests for regression coefficients in high dimensional partially linear Models. The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed. Then, the authors propose an empirical likelihood method to test regression coefficients. The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis. In addition, the method is extended to test with nuisance parameters. Simulations show that the proposed method have a good performance in control of type-I error rate and power. The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma (SKCM).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yan Liu, Mingyang Ren & Sanguo Zhang

  2. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, 100190, China

    Yan Liu, Mingyang Ren & Sanguo Zhang

Authors
  1. Yan Liu
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  2. Mingyang Ren
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  3. Sanguo Zhang
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Corresponding author

Correspondence to Sanguo Zhang.

Additional information

This work is supported by the University of Chinese Academy of Sciences under Grant No. Y95401TXX2, Beijing Natural Science Foundation under Grant No. Z190004, and Key Program of Joint Funds of the National Natural Science Foundation of China under Grant No. U19B2040.

This paper was recommended for publication by Editor DONG Yuexiao.

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Liu, Y., Ren, M. & Zhang, S. Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models. J Syst Sci Complex 34, 1135–1155 (2021). https://doi.org/10.1007/s11424-020-9260-3

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  • DOI: https://doi.org/10.1007/s11424-020-9260-3

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