A new test for part of high dimensional regression coefficients

It is well known that the F-test breaks down completely when the dimension of covariates exceeds the sample size. This paper proposes a new test for part of regression coefficients in high dimensional linear models. Under the high dimensional null hypothesis and various scenarios of the alternative, we derive the asymptotic distribution of the proposed test statistic, which allows power evaluation of the test. Through simulation studies, we demonstrate good finite-sample performance of the proposed test in comparison with the existing methods. The practical utility of our method is illustrated by a real data example.