Generalized ridge estimator and model selection criterion in multivariate linear regression

TL;DR

This paper introduces new model selection criteria for multivariate linear regression based on generalized ridge estimators, which outperform traditional methods in risk and model identification.

Contribution

The paper develops novel model selection criteria using generalized ridge estimators that dominate maximum likelihood estimators under key risk measures, with proven consistency and favorable properties.

Findings

Proposed criteria have smaller risks than MLE-based criteria.

Criteria are consistent and can identify the true model under certain conditions.

Experimental results confirm the superiority of the new criteria.

Abstract

We propose new model selection criteria based on generalized ridge estimators dominating the maximum likelihood estimator under the squared risk and the Kullback-Leibler risk in multivariate linear regression. Our model selection criteria have the following favorite properties: consistency, unbiasedness, uniformly minimum variance. Consistency is proven under an asymptotic structure $\frac{p}{n}\to c$ where $n$ is the sample size and $p$ is the parameter dimension of the response variables. In particular, our proposed class of estimators dominates the maximum likelihood estimator under the squared risk even when the model does not include the true model. Experimental results show that the risks of our model selection criteria are smaller than the ones based on the maximum likelihood estimator and that our proposed criteria specify the true model under some conditions.