Nonparametric multivariate rank tests and their unbiasedness

Abstract

Paper considers two sample multivariate testing problem. We construct several rank tests, which are finite-sample unbiased against a broad class of location/scale alternatives and are finite-sample distribution free, under the hypothesis and alternatives.

Everyone of them is locally most powerful against a specific alternative of the Lehmann type. Their powers against some alternatives are numerically compared with each others and with other rank and classical tests.

The question of affine invariance of two-sample multivariate tests is discussed.

Keywords

• Affine invariance
• Contiguity
• Kolmogorov-Smirnov test
• Lehmann alternatives
• Liu-Singh test
• Psi-test
• Savage test