A new location-scale test based on a combination of the ideas of Levene and Lepage

Neuhäuser, Markus; Leuchs, Ann-Kristin; Ball, Dorothee

doi:10.1002/bimj.201000162

Cited by 15 publications

(6 citation statements)

References 39 publications

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“…Duran et al (1976) obtained asymptotic distribution and investigated asymptotic relative efficiency. Statisticians have also considered the applications and modifications of the simultaneous test (Murakami, 2007;Neuhäuser et al, 2011); in addition, Park (2012) also proposed the simultaneous tests with the combining functions.…”

Section: Discussionmentioning

confidence: 99%

Simultaneous Tests with Combining Functions under Normality

Park

2015

CSAM

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We propose simultaneous tests for mean and variance under the normality assumption. After formulating the null hypothesis and its alternative, we construct test statistics based on the individual p-values for the partial tests with combining functions and derive the null distributions for the combining functions. We then illustrate our procedure with industrial data and compare the efficiency among the combining functions with individual partial ones by obtaining empirical powers through a simulation study. A discussion then follows on the intersectionunion test with a combining function and simultaneous confidence region as a simultaneous inference; in addition, we discuss weighted functions and applications to the statistical quality control. Finally we comment on nonparametric simultaneous tests.

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Section: Discussionmentioning

confidence: 99%

Simultaneous Tests with Combining Functions under Normality

Park

2015

CSAM

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“…The Lepage (L) test is a sum of squares of the standardized Wilcoxon-Mann-Whitney and Ansari-Bradley statistics. Sometimes a replacement of one of those summands by another test statistic is proposed, e.g., the Ansari-Bradley statistics was replaced with the Wilcoxon rank-sum applied to the Levene's transformation by Neuhäuser et al (2011) and with the Mood statistics by Ross et al (2012).…”

Section: Introductionmentioning

confidence: 99%

“…When applied to densities with nonzero skewness, the Lepage and Lepage-type tests were analyzed by Kössler (2006). The next example of studies for skewed distributions was presented in Neuhäuser et al (2011) where apart from symmetrical, also exponential and χ 2 distributions were analyzed in reference to size and power properties of the location-scale test based on idea of Levene and Lepage. In Marozzi (2013) the Cucconi test was compared to other five nonparametric location-scale tests through extensive studies for many symmetrical distributions and for asymmetrical exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

The Cucconi Test for Location-scale Alternatives in Application to Asymmetric Hydrological Variables

Rutkowska

Banasik

2015

Communications in Statistics - Simulation and Computation

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To identify location-scale trends, which environmental data often exhibit, location-scale tests have to be addressed. The aim of this article was to estimate size and power of the Cucconi rank-based test when applied to various skewed distributions, typical in hydrology. Results of the Monte Carlo simulation revealed great power for series with low coefficient of variation, time of change close to the middle, not very heavy tail, and with length of at least 60. Comparison to the Lepage test discovered larger usefulness of the Cucconi test for short series and change close to the middle. Several practical applications were presented.

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“…A test based on Lepage's proposal but using Mood's test statistic for the scale parameter was presented by Duran et al (1976). Later, Lepage's procedure was reviewed and discussed extensively by many authors (Murakami, 2007;Neuhauser, Leuchs and Ball, 2011). Marozzi (2008) considered the problem of location and scale using a nonparametric combination procedure proposed by Pesarin (2001).…”

Section: Introductionmentioning

confidence: 99%

On Permutation Location–scale Tests

Polko-Zając

2019

Statistics in Transition New Series

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Statisticians are constantly looking for methods of statistical inference that would be both effective and would require meeting as few assumptions as possible. Permutation tests seem to fit here, as using them makes it possible to perform statistical inference in situations where classical parametric tests do not work. Permutation tests appear to be comparably powerful to parametric tests, but require meeting fewer assumptions, e.g. regarding the size of the sample or the from of distribution of the tested variable in a population. The presented tests make it possible to verify the overall hypothesis about the identity of both location and scale parameters in the studied populations. In literature, the Lepage test and the Cucconi test are most often referred to in this context. The paper considers various forms of test statistics, and presents a simulation study carried out to determine the size and power of the tests under normality. As the study demonstrated, the advantage of the proposed method is that it can be applied to small-size samples. A nonparametric, complex procedure was used to assess the overall ASL (achieved significance level) value by applying the permutation principle. For comparative purposes, the results for the permutation Lepage test and the permutation Cucconi test are also presented.

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A new location-scale test based on a combination of the ideas of Levene and Lepage

Cited by 15 publications

References 39 publications

Simultaneous Tests with Combining Functions under Normality

Simultaneous Tests with Combining Functions under Normality

The Cucconi Test for Location-scale Alternatives in Application to Asymmetric Hydrological Variables

On Permutation Location–scale Tests

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