Generalized F test for high dimensional linear regression coefficients

To test the regression coefficients of linear models, the conventional F-test has been suggested. This paper investigates the performance of the generalized F-test for testing regression coefficients in high dimensional linear regression under the case of p/n⟶ρ(0<ρ<1). The asymptotic normality of generalized F-statistic is obtained under some regular conditions, and then the power of the F-test is derived. Some comparisons and an illustrated example are also presented.