Hypothesis testing for regional quantiles

- The hypothesis testing detects significant covariates for a given quantile region.
- The proposed score test admits normal approximations for high dimensional cases.
- The test can provide higher power than existing tests designed for a single quantile.

We consider the problem of testing significance of predictors in quantile regression, where the sample size n and the number of predictors are allowed to increase together. Unlike the quantile regression analysis for the τth quantile at a given τ∈(0,1), we aim to detect any covariate that is significant for the conditional quantiles at any level of interest in a given region, τ∈Δ. We use B-splines to approximate the quantile functions as τ varies and consider the composite quantile regression to estimate the parameters. The proposed score-type test admits normal approximations even in the presence of high dimensional variables. Through numerical examples, we demonstrate that the proposed test can provide higher power than existing tests designed for single quantile levels.