Nonparametric tests for two-sample dispersion problems: Problems with known dispersion centers

Abstract

Nonparametric two-sample dispersion problems with fixed dispersion centers based on the m-ordering are discussed. It turns out that permutation and conditional rank tests are appropriate procedures for testing these problems. While all procedures which do not depend on the dispersion centers as common linear rank tests among others are in general not unbiased and not consistent, these conditional tests have such properties under very mild regularity conditions. Furthermore, they are locally optimal and locally asymptotic optimal with respect to appropriate one-parameter subclasses of alternatives.

Keywords:

• Nonparametric dispersion models
• μ-ordering
• spread-ordering
• permutation tests
• conditional rank tests
• asymptotic normality
• consistency