Model Selection Criteria for Misspecified Quantile Regression Models in High Dimensions

• Activity Number: 450
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 3:05 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alexander Giessing* and Xuming He
• Companies: University of Michigan and University of Michigan
• Keywords: Bayesian information criterion ; model selection ; high-dimensional data ; misspecified models

Abstract

Model selection is a key conceptual tool for performing dimension reduction in high-dimensional statistics. Most existing work on high-dimensional quantile regression assumes that the model is correctly specified. Yet, in practice, misspecification of the quantile regression function is unavoidable. We consider an information theoretic approach to the problem of selecting a quantile function from a family of misspecified quantile regression models. We propose two novel Akaike (AIC) and Bayesian (BIC) information criteria that are based on non-asymptotic expansions of the asymmetric Laplace log-likelihood. Both criteria allow insightful decompositions into penalties on model complexity, model dimensionality, and model misspecification. Extensive numerical studies demonstrate the advantage of those criteria over some state of the art alternatives for model selection in high-dimensional quantile regression. We also demonstrate through empirical work the fine performance of the proposed approach.