Generalized 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.