Constrained quantile regression and heteroskedasticity

Quantile crossings do not occur so infrequently as to be declared virtually nonexistent; instead, researchers often have to face the quantile hyperplanes intersections issue, particularly with small and moderate sample sizes. Quantile crossings are particularly disturbing when one considers the estimation of the sparsity function. This, in fact, has a prominent role in determining the asymptotic properties of estimators and in testing the homoskedasticity of residuals. The primary goal of this study is to show that constrained quantile regression can improve conjoint results. We introduce a new method to this end. Furthermore, we carry out a comparison between the Wald test of homoskedasticity, computed by both neglecting and including quantile crossings. Real and simulated data illustrate the finite-sample performance of both versions of the test. Our experiments support the insight that considering monotonicity constraints is relatively rewarding when heteroskedasticity has to be accurately diagnosticated.