A constrained minimum criterion for model selection

TL;DR

This paper introduces a hypothesis test-based model selection criterion for sparse linear models that is consistent and balances false active and inactive rates, applicable with methods like lasso.

Contribution

It proposes a new model selection criterion that is theoretically consistent and can be integrated with existing methods such as lasso.

Findings

The criterion is consistent, with probability of selecting the true model approaching one.

It effectively balances false active and false inactive rates.

Numerical comparisons and applications demonstrate its accuracy and advantages.

Abstract

We propose a hypothesis test based model selection criterion for the best subset selection of sparse linear models. We show it is consistent in that the probability of its choosing the true model approaches one and the parameter values of its chosen model converge in probability to that of the true model as the sample size goes to infinity. This criterion is capable of controlling the balance between the false active rate and false inactive rate of the selected model, and it can be applied with other methods of model selection such as the lasso. We also demonstrate its accuracy and advantages with a numerical comparison and an application.