Some<i>c</i>-sample rank tests of homogeneity against umbrella alternatives with unknown peak

Kössler, Wolfgang

doi:10.1080/00949650412331320882

Cited by 14 publications

(9 citation statements)

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“…If the first or last location shift is expected to be much higher than the remaining shifts, and the remaining location shifts are expected to be approximately equal, both the Chen-Wolfe and Mack-Wolfe tests are recommended for use. It has been also shown (Kössler 2006) that generally the Hettmansperger-Norton-type test performs best, closely followed by the Chen-Wolfe-type test and the Shi-type test. Recently, Pan (2008) proposed a non-parametric distributionfree confidence procedure for umbrella orderings by constructing a random confidence subset of the ordered treatments such that it contains all the unknown peaks (optimal treatments) of an umbrella ordering with any pre-specified confidence level.…”

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confidence: 95%

A permutation test for umbrella alternatives

Basso

Salmaso

2009

Stat Comput

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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

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confidence: 95%

A permutation test for umbrella alternatives

Basso

Salmaso

2009

Stat Comput

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“…In Table 1, values of APE/I(f) are displayed in the case of equal sample sizes and k = 5, p = 2 for various test statistics. The weights { wi} are indicated in each case using results of Kossler (2006). It can be seen that the statistic Sp compares well in all cases.…”

Section: T H E O R E Mmentioning

confidence: 98%

“…See also Chen (1991) and, more recently, Millen & Wolfe (2005), who introduce modifications and exhibit a simulation study. Kossler (2006) compares the test statistics based on the statistics due to Chen and Wolfe, Hettmansperger and Norton, and Shi.…”

Section: The Construction Of the Test Statistics For Known Peakmentioning

confidence: 99%

“…Shi (1988) proposed a test statistic similar to Hettmansperger and Norton's, but using a different weighting scheme. Kossler (2006) generalized the test statistics due to Hettmansperger and Norton, Chen and Wolfe, and Shi by using score functions instead of ranks when the location of the peak is unknown. He concluded from an extensive simulation study that the Hettmansperger-Norton type test performed best overall followed closely by the Chen-Wolfe type test and the Shi-type test.…”

Section: The Construction Of the Test Statistics For Known Peakmentioning

confidence: 99%

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Nonparametric tests of hypotheses for umbrella alternatives

Alvo

2008

Can J Statistics

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MSC 2000: Primary 62G 10; secondary 62G20. Abstract:The author proposes a general method for constructing nonparametric tests of hypotheses for umbrella alternatives. Such alternatives are relevant when the treatment effect changes in direction after reaching a peak. The author's class of tests is based on the ranks of the observations. His general approach consists of defining two sets of rankings: the first is induced by the alternative and the other by the data itself. His test statistic measures the distance between the two sets. The author determines the asymptotic distribution for some special cases of distances under both the null and the alternative hypothesis when the location of the peak is known or unknown. He shows the good power of his tests through a limited simulation study. Tests d'hypotheses non parametriques pour des contre-hypotheses parapluiesR h m t : L'auteur propose une mBthode gBnCrale de construction de tests non paramktriques pour des contre-hypothtses parapluies. De telles hypotheses sont pertinentes lorsque l'effet de traitement chahge de direction apres avoir atteint un sommet. La classe de tests de l'auteur est fond& sur les rangs des observations. Son approche gknkrale fait intervenir deux ensembles de rangs : le premier dkoule de la contre-hypothtse et le second Bmane des donn&s elles-memes. L a statistique de son test mesure la distance entre les deux ensembles. L'auteur en dCtermine la loi asymptotique dans quelques cas s e i a u x de distance sous l'hypothtse nulle et sous la contre-hypothtse selon que la localisation du sommet est connue ou non. I1 illustre la bonne puissance de ses tests au moyen d'une petite Btude de simulation.

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“…Chen (1993) and Chen and Wolfe (1993) discussed comparing umbrella pattern treatment effects with a control in a one-way layout. Kössler (2006) considered k-sample rank tests of homogeneity against umbrella alternatives with the unknown peak. For the multivariate k-sample data setting, that is, when p > 1, the multivariate generalisation of the first case (discussed above) is known as the Kruskal-Wallis-type (KW-type) test (in the sense that the samples are variously ordered).…”

Section: Introductionmentioning

confidence: 99%