Interval quantile correlations with applications to testing high-dimensional quantile effects

Abstract

In this article, we propose interval quantile correlation and interval quantile partial correlation to measure the association between two random variables over an interval of quantile levels. We construct efficient estimators for the proposed correlations, and establish their asymptotic properties under the null and alternative hypotheses. We further use the interval quantile partial correlation to test for the significance of covariate effects in high-dimensional quantile regression when a subset of covariates are controlled. We calculate marginal interval quantile partial correlations for each covariate, then aggregate them to construct a sum-type test statistic. The null distribution of our proposed test statistic is asymptotically standard normal. We use extensive simulations and an application to illustrate that our proposed test, which pools information across an interval of quantile levels to enhance power performances, is very effective in detecting quantile effects.