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.
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