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

LIU Yan · REN Mingyang · ZHANG Sanguo   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; KeyLaboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100190,China. Email: liuyan172@mails.ucas.ac.cn; renmingyang17@mails.ucas.ac.cn; sgzhang@ucas.ac.cn.
  • Online:2021-06-25 Published:2021-03-11

LIU Yan · REN Mingyang · ZHANG Sanguo. Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models[J]. Journal of Systems Science and Complexity, 2021, 34(3): 1135-1155.

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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