KOO Approach for Scalable Variable Selection Problem in Large-dimensional Regression

An important issue in many multivariate regression problems is to eliminate candidate predictors with null predictor vectors.In large-dimensional (LD) setting where the numbers of responses and predictors are large, model selection encounters the scalability challenge.Knock-one-out (KOO) statistics hold promise to meet this challenge.In this paper, the almost sure limits and the central limit theorem of the KOO statistics are derived under the LD setting and mild distributional assumptions (finite fourth moments) of the errors by random matrix theory.These theoretical results guarantee the strong consistency of a subset selection rule based on the KOO statistics with a general threshold.For enhancing the robustness of the selection rule, we also propose a bootstrap threshold for the KOO approach.