Nonparametric Multivariate Rank Tests and their Unbiasedness

0383505 - ÚI 2013 RIV NL eng J - Článek v odborném periodiku
Jurečková, J. - Kalina, Jan
Nonparametric Multivariate Rank Tests and their Unbiasedness.
Bernoulli. Roč. 18, č. 1 (2012), s. 229-251. ISSN 1350-7265. E-ISSN 1573-9759
Grant ostatní: GA ČR(CZ) GA201/09/0133; GA AV ČR(CZ) IAA101120801; GA MŠk(CZ) LC06024
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: affine invariance * contiguity * Kolmogorov–Smirnov test * Lehmann alternatives * Liu–Singh test * Psi test * Savage test * two-sample multivariate model * unbiasedness * Wilcoxon test
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum
Impakt faktor: 0.935, rok: 2012

Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17 (1965) 261–263]; he found an alternative against which the Wilcoxon test is not unbiased. The problem is even more serious in multivariate models. When testing the hypothesis against an alternative which fits well with the experiment, it should be verified whether the power of the test under this alternative cannot be smaller than the significance level. Surprisingly, this serious problem is not frequently considered in the literature. The present paper considers the 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. Each of them is locally most powerful against a specific alternative of the Lehmann type. Their powers against some alternatives are numerically compared with each other and with other rank and classical tests. The question of affine invariance of two-sample multivariate tests is also discussed.
Trvalý link: http://hdl.handle.net/11104/0213418