325 research outputs found
A Response to Anderson\u27s (2013) \u3cem\u3eConceptual Distinction between the Critical p value and Type I Error Rate in Permutation Testing\u3c/em\u3e
No full textPesarin and Bonnini respond to Anderson\u27s (2013) Conceptual Distinction between the Critical p value and Type I Error Rate in Permutation Testin
Permutation Anderson-Darling type and moment-based test statistics for univariate ordered categorical data
No full textIn this article we consider permutation methods for univariate testing on ordered variables based on the nonparametric combination of permutation dependent tests (Pesarin, 2001).
Several solutions have been proposed to cope with univariate testing problems on ordered categorical data, most of which are based on the restricted maximum likelihood ratio test. These solutions are generally criticized, because the degree of accuracy of their asymptotic null and alternative distributions is difficult to assess and to characterize.
By working within the nonparametric combination of dependent permutation tests (NPC), it is possible to find exact solutions to that kind of problems. We examine some of these solutions and discuss one more new exact solution based on simultaneous analysis of a finite set of sampling moments of ranks, or general scores, assigned to ordered classes and processed by the NPC method.
A simulation study analyzes the empirical power of the considered NPC solutions compared with the Wilcoxon test with ties correction. The new permutation test based on Fisher's combination of sampling moments shows a good behavior in power in all considered situations both for balanced and unbalanced sample sizes
Fortunato Pesarin: A Statistician for Complex Problems
No full textFortunato Pesarin is one of the most prominent figures in Italian statistics over the last fifty years. In his long life as a scholar he has documented the developments of world statistics that came out of the Second World War and has spread them through the Italian academic world and to the many generations of students who have attended his university lectures. His contributions have been characterized by research of new methodological solutions, often outside the line of existing one, at the cost of not being fully understood
A multivariate extension of union-intersection permutation solution for two-sample testing
No full textThere are mainly two approaches to compare effects of two treatments: following the intersection–union principle (IU) or following the union–intersection principle (UI). The two approaches substantially differ by the role stated from the null and alternative hypotheses, which are mirror inverted. In particular, the IU principle considers as alternative hypothesis that the effect of a new treatment lies within a given interval around that of the comparative treatment, whereas the UI principle considers as alternative hypothesis that this effect lies outside that interval. Pesarin et al. recently discussed these two solutions and proposed a permutation approach based on the union-intersection framework. Often in pharmaceutical experiments it happens that more than one variable have to be simultaneously considered, in order to assess dissimilarity of two treatments. Generally this kind of problem is difficult to face outside the nonparametric framework, particularly due to the complex dependency structure among several variables and consequent related partial tests. Thus, the purpose of this article is to extend the existing UI-permutation solution toward a general multidimensional setting. In order to explain the performance and the applicability of the proposed method, a simulation study and application example are also shown
On the Weak Consistency of Permutation Tests
No full textConsistency of some nonparametric tests with real variables has been studied by several authors under the assumption that population variance is finite and/or in the presence of some violations of the data exchangeability between samples. Since main inferential conclusions of permutation tests concern the actual dataset, where sample sizes are held fixed, we consider the notion of consistency in the weak version (in probability). Here, we characterize weak consistency of permutation tests assuming population mean is finite and without assuming existence of population variance. Moreover, since permutation test statistics do not require to be standardized, we do not assume that data are homoscedastic in the alternative. Several application examples to mostly used test statistics are discussed. A simulation study and some hints for robust testing procedures are also presented
- …
