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).

本文考虑对高维部分线性模型中的回归系数进行测试。作者首先使用B样条方法估计未知的平滑函数，以便可以线性表示它。然后，作者提出了一种经验似然方法来检验回归系数。作者在零假设下得出了具有两个自由度的拟议检验统计量的渐近卡方分布。另外，该方法被扩展为使用讨厌的参数进行测试。仿真表明，该方法在控制I类错误率和功率方面具有良好的性能。所提出的方法还用于分析皮肤皮肤黑色素瘤（SKCM）的数据。