Directional testing for high dimensional multivariate normal distributions

Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when number of components p same asymptotic order as sample size n, standard inferential techniques are generally inadequate conduct hypothesis testing on mean vector and/or covariance matrix. Within several prominent frameworks, we propose then draw reliable conclusions via a directional test. We show that under null p-value exactly uniformly distributed even provided conditions existence maximum likelihood estimate model satisfied. Extensive simulation results confirm theoretical findings across different values p∕n, and test outperforms not only usual first higher-order finite-p solutions but also alternative methods tailored high dimensional settings. Simulation indicate power performance tests depends specific hypothesis.