Vertical quantile comparison functions estimation in location scale families

Abstract Two-sample location-scale refers to a situation in which a pair of random variables are linearly related to a base random variable that has mean 0 and variance 1. Using a formulation that leverages the location-scale structure, a semiparametric estimator of the vertical quantile comparison function is proposed and its large-sample properties are derived. Its efficacy relative to that of a nonparametric estimator as well as its robustness to departures from location-scale models is investigated through numerical studies.