In several application fields, e.g. genetics, image and functional analysis, several biomedical and social experimental and observational studies, etc. it may happen that the number of observed variables is much larger than that of subjects. It can be proved that, for a given and fixed number of subjects, when the number of variables increases and the noncentrality parameter of the underlying population distribution increases with respect to each added variable, then power of multivariate permutation tests based on Pesarin's combining functions [Pesarin, F. (2001), Multivariate Permutation Tests with Applications in Biostatistics, New York: Wiley, Chichester] is monotonically increasing. These results confirm and extend those presented by [Blair, Higgins, Karniski and Kromrey (1994), 'A Study of Multivariate Permutation Tests which May Replace Hotelling's T2 Test in Prescribed Circumstances', Multivariate Behavioral Research 29, 141-163]. Moreover, they allow us to introduce the property of finite-sample consistency for those kinds of combination-based permutation tests. Sufficient conditions are given in order that the rejection rate converges to one, for fixed sample sizes at any attainable -values, when the number of variables diverges. A simulation study and a real case study are presented
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.