Likelihood ratio tests under model misspecification in high dimensions

We investigate the likelihood ratio test for a large block-diagonal covariance matrix with an increasing number of blocks under null hypothesis. While so far statistic has only been studied normal populations, we establish that its asymptotic behavior is invariant much larger class distributions. This implies robustness against model misspecification, which common in high-dimensional regimes. Demonstrating flexibility our approach, additionally normality log-likelihood equality many sample matrices uncertainty. A simulation study and analysis data set from psychology emphasize usefulness findings.