Linear regression model selection using p-values when the model dimension grows

TL;DR

This paper introduces a new p-value-based model selection method for linear regression that remains consistent as the model dimension grows, outperforming traditional criteria like AIC and BIC in simulations.

Contribution

It proposes a novel p-value-based criterion for linear regression model selection with proven consistency in high-dimensional settings.

Findings

The new method is consistent even when the number of models increases with sample size.

Simulation results show competitive performance compared to AIC and BIC.

The approach is theoretically justified for growing model dimensions.

Abstract

We consider a new criterion-based approach to model selection in linear regression. Properties of selection criteria based on p-values of a likelihood ratio statistic are studied for families of linear regression models. We prove that such procedures are consistent i.e. the minimal true model is chosen with probability tending to 1 even when the number of models under consideration slowly increases with a sample size. The simulation study indicates that introduced methods perform promisingly when compared with Akaike and Bayesian Information Criteria.