Oral Prelim: Michael Hornstein, A Matrix-Variate Approach to Large-Scale Inference with Dependent Observations

Large-scale inference involves testing many hypotheses simultaneously, for example testing for differences in mean expression levels of thousands of genes. Correlations between genes and between individuals may both be present in the data. The matrix-variate normal distribution models data in which correlations exist between both rows and columns. We investigate the performance of a likelihood ratio test for matrix-variate data in the setting of two-group hypothesis testing. Via simulation, we compare the likelihood ratio test to a Wald test and to a previously proposed approach based on decorrelating the data prior to performing hypothesis tests. Furthermore, we apply the likelihood ratio test to a microarray data set previously studied by Efron.