A New Approach to Function-Based Hypothesis Testing in Location-Scale Families

Abstract

Motivated by two applications in the mining industry, we introduce a new approach to testing the hypothesis that two-sampled distributions are simply location and scale changes of one another. The test, applicable to both paired data and two-sample data, is based on the empirical characteristic function. More conventional techniques founded on the empirical distribution function suffer from serious drawbacks when used to test for location-scale families. In the motivating applications, knowing that the distributions differ only in location and scale has significant operational and economic advantages, enabling protocols for one type of data to be applied directly to another. Supplementary material in the form of Matlab code is available online.

KEY WORDS:

• Bootstrap
• Empirical characteristic function
• Testing for differences between mean
• Testing in paired samples
• Tests based on empirical distribution function
• Two-sample tests

ACKNOWLEDGMENTS

Hall’s work was supported by an Australian Research Council grant to the University of Melbourne, and an NSF grant to UC Davis. Lombard’s work was supported by a grant from the National Research Foundation of South Africa. Potgieter’s work was supported by NSF grant DMS-0914951.