Resampling, subsampling, and quantile regression

This chapter focuses on subsampling and resampling methods to further analyze the characteristics of the quantile regression estimator. It considers the elemental sets approach, which provides a very intuitive tool to compare OLS and quantile regressions. The chapter discusses alternative interpretations of the quantile regression estimators, based respectively on the p-dimensional subsets and on the use of bootstrap when the former approach is unfeasible due to the large size of the sample. It reports a brief review of the asymptotic distribution of the non-extreme quantile regression estimator for comparison's sake. The asymptotics of intermediate- and central-order quantile regression estimators could be obtained by modifying the extreme-value approach. The chapter analyzes an additional quantile regression approach relying on bootstrap, the quantile treatment effect (QTE) estimator, which is implemented to evaluate the impact of a treatment or a policy.