  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. 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. Simulation results support our conclusions and
demonstrate the selection probabilities by the KOO approach with the bootstrap
threshold outperform the methods using Akaike information threshold, Bayesian
information threshold and Mallow's C$_p$ threshold. We compare the proposed KOO
approach with those based on information threshold to a chemometrics dataset
and a yeast cell-cycle dataset, which suggests our proposed method identifies
useful models.
