A key problem in many multivariate regression problems is eliminating candidate predictors with null predictor vectors. Large dimensionality (LD) settings with large numbers of responses and predictors present scalability challenges in model selection. Knockout (KOO) statistics have the potential to solve this challenge. In this paper, we derive the strong consistency and central limit theorem of the KOO statistic under the LD setting and the moderate distribution assumption of the error (finite 4 moments). These theoretical results lead us to propose a subset selection rule based on his KOO statistics using bootstrap thresholds. Simulation results support our conclusions and show that the selection probability by his KOO approach using bootstrap thresholds outperforms methods using Akaike information threshold, Bayesian information threshold and Mallow’s C$_p$ threshold. indicates that there is We compare the proposed KOO approach with information threshold-based approaches on the chemometrics dataset and the yeast cell cycle dataset. This suggests that the proposed method identifies useful models.

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