Variable selection in multiple regression with random design

TL;DR

This paper introduces a new variable selection method for multiple regression with random predictors, focusing on estimating permutation and dimensionality to improve selection consistency.

Contribution

It presents a novel criterion-based approach that reduces variable selection to permutation and dimensionality estimation, with proven consistency.

Findings

The proposed method is consistent in variable selection.

Simulation results demonstrate competitive performance.

Comparison with existing methods shows advantages in certain scenarios.

Abstract

We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and dimensionality. Then, estimators for these parameters are proposed and the resulting method for selecting variables is shown to be consistent. A simulation study that permits to gain understanding of the performances of the proposed approach and to compare it with an existing method is given.