Nonparametric tests for scale and location

Abstract

We prove asymptotic normality of simple linear rank statistics when the observations have U-statistic structure. This type of statistic can be used for testing the location parameter and/or the scale parameter in a scale-location model. It is shown that the tests for the location parameter are asymptotically efficient under normality using a normal score function and are also as efficient as the t-test when the dimension of the kernel function tends to infinity and when Wilcoxon scores are used. For scaling parameters we propose a generalization of tests by Lehmann and Moses for scale effects. We describe a simulation study which shows that these new tests perform better than the ones previously used.

Keywords:

• Linear rank statistic
• U-statistic
• two sample problem for location-scale models
• Pitman efficiency

AMS Subject Classification:

• 62G10
• 62620
• 60F05