Minimum Predictive Risk Subspace Selection in Misspecified Quantile Regressions

• Activity Number: 308
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Royal Statistical Society
• Author(s): Alexander Giessing* and Xuming He
• Companies: University of Michigan and University of Michigan
• Keywords: Quantile Regression ; Variable Selection ; AIC ; BIC ; Misspecified Model

Abstract

We introduce the concept of minimum predictive risk subspaces for variable selection in high-dimensional misspecified quantile regressions. This framework is natural in situations in which the true quantile functions are unknown or stipulating the existence of a single true quantile function is too restrictive. Our selection procedure adjusts the selection bias associated with the relative entropy of the candidate predictors. Under mild conditions on the quantile functions, the new procedure is shown to consistently select the set of predictors that span a low-dimensional linear subspace with minimal predictive risk. Furthermore, the selection procedure is quantile-adaptive and can therefore identify different minimum predictive risk subspaces for different quantiles. This property proves particularly effective when analyzing heteroscedastic and skewed data. Numerical studies demonstrate the advantages of the new method on the basis of various misspecified quantile regressions models.