Generalized F-Test for High Dimensional Regression Coefficients of Partially Linear Models

摘要

This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic.In the partially linear model,the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions.During this procedure,the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test.The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p ∈ (0,1) without normality assumption.The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models.Through simulation studies,the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results.The practical utility of our method is illustrated by a real data example.