A Minimum Distance Estimation Approach to the Two-Sample Location-Scale Problem

As reported by Kalbfleisch and Prentice (1980), the generalized Wilcoxon test fails to detect a difference between the lifetime distributions of the male and female mice died from Thymic Leukemia. This failure is a result of the test's inability to detect a distributional difference when a location shift and a scale change exist simultaneously. In this article, we propose an estimator based on the minimization of an average distance between two independent quantile processes under a location-scale model. Large sample inference on the proposed estimator, with possible right-censorship, is discussed. The mouse leukemia data are used as an example for illustration purpose.