1,721,412 research outputs found
Combination-Based Permutation Tests: Equipower Property and Power Behaviour in Presence of Correlation
No full textMultivariate combination-based permutation tests have been widely used in many complex problems. In this paper we focus on the equipower property, derived directly from the finite sample consistency property, and we analyze the impact of the dependency structure on the combined tests. At first, we consider the finite sample consistency property which assumes sample sizes are fixed (and possibly small) and considers on each subject a large number of informative variables. Moreover, since permutation test statistics do not require to be standardized, we need not assuming that data are homoscedastic in the alternative. The equipower property is then derived from these two notions: consider the unconditional permutation power of a test statistic T for fixed sample sizes, with V ≥ 2 independent and identically distributed variables and fixed effect δ, calculated in two ways: i) by considering two V-dimensional samples sized m 1 and m 2, respectively; ii) by considering two unidimensional samples sized n 1 = Vm 1 and n 2 = Vm 2, respectively. Since the unconditional power essentially depends on the non-centrality induced by T, and two ways are provided with exactly the same likelihood and the same non-centrality, we show that they are provided with the same power function, at least approximately. As regards both investigating the equipower property and the power behaviour in presence of correlation we performed an extensive simulation study
Testing for Umbrella Alternatives with Application to the Evaluation of Degree-Granting Sessions
No full textPermutation testing for goodness of fit and stochastic ordering
No full textProblems of testing for ordered categorical variables are of great interest in
many application disciplines, where a finite number of Q 1 of such variables are observed
on each individual unit (Pesarin and Salmaso (2006) (Pesarin and Salmaso, 2010a) and
(Pesarin and Salmaso, 2010b)). In particular, Goodness of Fit tests are used to measuring
how well do the observed data correspond to the assumption model. Several parametric
solutions to univariate case have been proposed in literature. In particular, when dealing
with categorical variables, the most used methods are Pearson’s Chi-squared and Deviance
statistic. However, these methods, usually based on the restricted maximum likelihood ratio
test, are generally criticized because their asymptotic null and alternative distributions are
mixtures of chi-squared variables whose weights essentially depend on underlying population
distribution F and so the related degree of accuracy is difficult to assess and to characterize;
thus their use when F is unknown is somewhat questionable in practice. Moreover, is well
known the difficulty or impossibility to use them in multivariate cases. In many situations
it can be of interest testing for a set of restricted alternatives to H0 (Kim and Foutz (1997)
and Chapman (1958)). In these cases we can refer to Stochastic Ordering. Parametric
solutions don’t allow this kind of tests. By working within the Non-parametric combination
of dependent permutation tests, it is possible to find exact solutions to these problems.
The NPC approach works as a general methodology for most multivariate situations, as for
instance in cases where sample sizes are smaller than the number of observed variables, or
where there are non-ignorable missing values, or when some of the variables are categorical
(ordered and nominal) and others are quantitative and in many other complex situations.
In this work, NPC tests for stochastic dominance are presented, both for two sample
directional testing and for testing for a stochastic ordering in a multivariate setting. A
simulation study is reported to show the NPC approach efficacy
A permutation test for umbrella alternatives
No full textThere is a wide variety of stochastic ordering problems where K groups (typically ordered with respect to time) are observed along with a (continuous) response. The interest of the study may be on finding the change-point group, i.e. the group where an inversion of trend of the variable under study is observed. A change point is not merely a maximum (or a minimum) of the time-series function, but a further requirement is that the trend of the time-series is monotonically increasing before that point, and monotonically decreasing afterwards. A suitable solution can be provided within a conditional approach, i.e. by considering some suitable nonparametric combination of dependent tests for simple stochastic ordering problems. The proposed procedure is very flexible and can be extended to trend and/or repeated measure problems. Some comparisons through simulations and examples with the well known Mack & Wolfe test for umbrella alternative and with Page's test for trend problems with correlated data are investigated
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