Model selection by cross-validation in an expectile linear regression

TL;DR

This paper develops a cross-validation based method for variable selection in expectile linear regression models with asymmetric errors, demonstrating its consistency and effectiveness through simulations and real data applications.

Contribution

It introduces a novel cross-validation approach for expectile regression that is proven to be consistent and superior to existing methods in variable selection.

Findings

The proposed method is consistent for fixed and growing numbers of variables.

Monte Carlo simulations show the method outperforms existing techniques.

Real data applications illustrate the practical usefulness of the approach.

Abstract

For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training set. For the model coefficients, the expectile or adaptive LASSO expectile estimators are calculated on the training set. These estimators will be used to calculate the cross-validation mean score (CVS) on the validation set. We show that the model that minimizes CVS is consistent in two cases: when the number of explanatory variables is fixed or when it depends on the number of observations. Monte Carlo simulations confirm the theoretical results and demonstrate the superiority of our estimation method compared to two others in the literature. The usefulness of the CV expectile model selection technique is illustrated by applying it to real data sets.