Variable Selection in Seemingly Unrelated Regressions with Random Predictors

TL;DR

This paper introduces a novel approach for variable selection in multivariate linear models with random predictors, emphasizing the separation of inference from selection and analyzing predictor uncertainty.

Contribution

It proposes a new post-inference model summarization method that accounts for predictor randomness in seemingly unrelated regressions.

Findings

Effective variable selection under predictor uncertainty

Decoupling inference from selection improves model reliability

Application demonstrates practical utility in asset pricing

Abstract

This paper considers linear model selection when the response is vector-valued and the predictors are randomly observed. We propose a new approach that decouples statistical inference from the selection step in a "post-inference model summarization" strategy. We study the impact of predictor uncertainty on the model selection procedure. The method is demonstrated through an application to asset pricing.