Projection quantile correlation and its use in high-dimensional grouped variable screening

Abstract

In this paper, we propose a new measure, called Projection Quantile Correlation (PQC), to detect quantile dependence between a response and multivariate predictors at a given quantile level. The PQC measure is free of tuning parameters, robust against heavy tailed distributions and outliers, and does not require moment conditions on the predictors. We obtain theoretical properties of the PQC and its empirical counterpart. We then use the measure to select the grouped predictors that contribute to the conditional quantile of the response for high-dimensional data with group structures. We also establish sure independent screening properties for the group screening method. We illustrate the finite sample performance of the proposed method through simulations and an application to a dataset.