Asymptotic theory of weighted F-statistics based on ranks

Akritas, MG; Stavropoulos, A; Caroni, C

dc.contributor.author	Akritas, MG	en
dc.contributor.author	Stavropoulos, A	en
dc.contributor.author	Caroni, C	en
dc.date.accessioned	2014-03-01T01:29:54Z
dc.date.available	2014-03-01T01:29:54Z
dc.date.issued	2009	en
dc.identifier.issn	1048-5252	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19398
dc.subject	Asymptotic theory	en
dc.subject	Factorial designs	en
dc.subject	Nonparametric hypotheses	en
dc.subject	Nonparametric models	en
dc.subject	Weighted F rank statistics	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	UNBALANCED FACTORIAL-DESIGNS	en
dc.subject.other	NONPARAMETRIC HYPOTHESES	en
dc.subject.other	TESTS	en
dc.title	Asymptotic theory of weighted F-statistics based on ranks	en
heal.type	journalArticle	en
heal.identifier.primary	10.1080/10485250802485528	en
heal.identifier.secondary	http://dx.doi.org/10.1080/10485250802485528	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	Using subspaces to describe the nonparametric null hypotheses introduced in Akritas and Arnold [Fully nonparametric hypotheses for factorial designs I: multivariate repeated measures designs, J. Amer. Statist. Assoc. 89 (1994), pp. 336-343.], leads to a natural extension of the models and the class of nonparametric hypotheses considered there. Nonparametric versions of all saturated or unsaturated parametric models for factorial designs, as well as nonparametric versions of all parametric hypotheses considered in such contexts, are included in the new formulation. To test these new hypotheses we introduce a new family of (mid-)rank statistics. The new statistics are modelled after the weighted F-statistics and are appropriate for (possibly) unbalanced designs with independent observations that can be heteroscedastic. Being rank versions of likelihood ratio statistics, the proposed statistics apply in situations where the Wald-type rank statistics of Akritas, Arnold and Brunner [Nonparametric hypotheses and rank statistics for unbalanced factorial designs, J. Amer. Statist. Assoc. 92 (1997), pp. 258-265.] have not been extended and are at least as efficient in the cases where both apply. We show that the new rank statistics converge in distribution to central chi-squared distributions under their respective null hypotheses. Finding the asymptotic distribution of statistics without a closed form expression requires a novel approach, which we introduce. A simulation study compares the achieved level and power of the new statistics with a number of competing procedures.	en
heal.publisher	TAYLOR & FRANCIS LTD	en
heal.journalName	Journal of Nonparametric Statistics	en
dc.identifier.doi	10.1080/10485250802485528	en
dc.identifier.isi	ISI:000262515100004	en
dc.identifier.volume	21	en
dc.identifier.issue	2	en
dc.identifier.spage	177	en
dc.identifier.epage	191	en