A multitest procedure for testing MTP2 for Gaussian distributions

Abstract

We present a new test for MTP2 for Gaussian distributions. Our test is based on multiple testing whether all coefficients are non-positive beyond the diagonal of the inverse covariance matrix. In the low dimensional case, we use test statistics based on the inverse empirical covariance matrix and for the high dimensional case, we apply correction of the glasso estimator (desparsified glasso estimator, van de Geer et al. (2014)). In a simulation study, we compare our test with the universal test (Wasserman, Ramdas, and Balakrishnan (2020)) and we check the power and control of the type I error of these tests.