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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