A permutation test for umbrella alternatives

Abstract

There 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

Nonparametric bootstrap tests of conditional independence in two-way contingency tables

“…Therefore we did not feel there was a need to increase the number of resamples and/or replications for our simulation study. Our use of the 1000/1000 setup also falls in line with the likes of Brombin and Salmaso [4] and Basso and Salmaso [2] which also use the same quantities of resamples and replications to reach their conclusions. Moreover in preliminary testing we found that using B = 500 produced overall results which is very similar to those of B = 1000 presented below, further indicating that 1000/1000 is more than enough to reach accurate bootstrap approximations in this setting.…”

Testing against umbrella or tree orderings for binomial proportions with an adaptation of an insect resistance case

“…For umbrella and tree orderings, Mack and Wolfe (1981) proposed a test statistic, which is a weighted linear combination of standardized Mann-Whitney statistics and provided its null distribution in a wide variety of settings, while Magel and Qin (2003) proposed a test that extends the Chen and Wolfe (1990) test with an unknown peak for use with ranked-set sample data, and Lee and Chen (2001) generalized the Chen-Wolfe test based on a weighted Kaplan-Meier statistic for the peak-unknown umbrella alternative with right-censored survival data and also generalized the Mack-Wolfe test for right-censored data. Basso and Salmaso (2011) considered an approach conditional on the observed data, while Pardo, Lu, and Franco-Pereira (2019) proposed two families of test statistics for testing simple and umbrella stochastic orderings.…”

nparcomp: AnRSoftware Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals

“…For example, optimal subset procedures and weighted methods controlling the familywise error rate are proposed by Finos and Salmaso (2005), Finos and Salmaso (2006) and Finos and Salmaso (2007). Permutation tests for umbrella alternatives and multivariate problems are considered in Basso and Salmaso (2011) and Pesarin and Salmaso (2012).…”