Small sample performance of quantile regression confidence intervals

Abstract

Since the introduction of regression quantiles for estimating conditional quantile functions there has been ongoing research into how best to construct confidence intervals for parameter estimates. The three main methods are direct estimation, rank test inversion and resampling methods. Kocherginsky et al. [Practical confidence intervals for regression quantiles, J. Comput. Graph. Statist. 14 (2005), pp. 41–55] gave an overview of some of the available procedures. Five years on, the aim of this paper is to revisit and extend their analysis, evaluating additional techniques with a focus on smaller sample sizes and more extreme conditional quantiles. In particular, we find the percentile bootstrap (pbs) to be an eminently viable alternative for confidence interval construction. We show that it provides empirical coverage probabilities generally as good as, or better than, the other more complex resampling methods. Furthermore, pbs confidence intervals typically exhibit smaller average lengths across a variety of models than those based on the rank inversion methods which, like the pbs, avoids explicitly estimating asymptotic variances.

Keywords:

• quantile regression
• confidence intervals
• simulation study
• bootstrap

AMS Subject Classifications :

• 62J99
• 62F40
• 62F25