The naive Bayes approach is one of the most popular methods used for classification. Nevertheless, how to test its statistical significance under an ultra-high-dimensional (UHD) setup is not well understood. To fill this important theoretical gap, we propose a novel testing statistic with a...

The problem of regression shrinkage and selection for multivariate regression is considered. The goal is to consistently identify those variables relevant for regression. This is done not only for predictors but also for responses. To this end, a novel relationship between multivariate...

Many statistical analysis procedures require a good estimator for the high dimensional covariance matrix or its inverse, the precision matrix. When the precision matrix is banded, the Cholesky-based method can often yield a good estimator for the precision matrix. One important aspect of this...

The problem of regression shrinkage and selection for multivariate regression is considered. The goal is to consistently identify those variables relevant for regression. This is done not only for predictors but also for responses. To this end, a novel relationship between multivariate...