Title: Most powerful test against high dimensional alternatives
Authors: Yi He - University of Amsterdam (Netherlands) [presenting]
Jiti Gao - Monash University (Australia)
Sombut Jaidee - Monash University (Australia)
Abstract: A quadratic test in high-dimensional linear regression models is proposed when the number of variables is comparable to, even larger than, the sample size. Using random matrix theory, we show that it has the optimal asymptotic power against non-sparse local alternatives. Our approach allows testing only a subset of coefficients but keeping some nuisance parameters in the estimation, and relaxes the Gaussian assumptions in the literature. Simulation results agree with our asymptotic theory.