Asymptotic distribution of rank statistics under dependencies with multivariate application

Thompson, Gerald L.

doi:10.1016/0047-259x(90)90045-j

Cited by 28 publications

(10 citation statements)

References 10 publications

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“…. ; t 2 is called a relative treatment effect of F is with respect to the average H. For example, the procedures considered by Brunner and Neumann (1982), Kepner and Robinson (1988), Thompson (1990Thompson ( , 1991, Brunner and Denker (1994) and by Akritas and Arnold (1994) are based on this nonparametric marginal model and on the relative treatment effects p is defined in (2). 3.…”

Section: Statistical Model and Treatment Effectsmentioning

confidence: 99%

Nonparametric Analysis of Ordered Categorical Data in Designs with Longitudinal Observations and Small Sample Sizes

Brunner¹,

Langer²

2000

Biom. J.

194

153

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Section: Statistical Model and Treatment Effectsmentioning

confidence: 99%

Nonparametric Analysis of Ordered Categorical Data in Designs with Longitudinal Observations and Small Sample Sizes

Brunner¹,

Langer²

2000

Biom. J.

194

153

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“…Munzel and Brunner's, as well as our approach for defining multivariate nonparametric tests is based on separate rankings of the different variables, as opposed to the case for Thompson [8,9] who proposed multivariate tests based on overall rankings across the variables. Using separate rankings has some important advantages.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric methods for unbalanced multivariate data and many factor levels

Harrar

Bathke

2008

Journal of Multivariate Analysis

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We propose different nonparametric tests for multivariate data and derive their asymptotic distribution for unbalanced designs in which the number of factor levels tends to infinity (large a, small n i case). Quasi gratis, some new parametric multivariate tests suitable for the large a asymptotic case are also obtained. Finite sample performances are investigated and compared in a simulation study. The nonparametric tests are based on separate rankings for the different variables. In the presence of outliers, the proposed nonparametric methods have better power than their parametric counterparts. Application of the new tests is demonstrated using data from plant pathology.

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“…Rank tests were available for some multivariate factorial designs. For example, Thompson [10,11] studied nonparametric tests based on overall ranking of data from balanced one-factor design assuming continuous distributions. Akritas and Arnold [12] and Akritas and Brunner [13] gave nonparametric tests using overall rankings of data from multivariate repeated measures designs allowing both discrete and continuous data.…”

Section: Introductionmentioning

confidence: 99%

Rank test for heteroscedastic functional data

Wang

Akritas

2010

Journal of Multivariate Analysis

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a b s t r a c tIn this paper, we consider (mid-)rank based inferences for testing hypotheses in a fully nonparametric marginal model for heteroscedastic functional data that contain a large number of within subject measurements from possibly only a limited number of subjects. The effects of several crossed factors and their interactions with time are considered. The results are obtained by establishing asymptotic equivalence between the rank statistics and their asymptotic rank transforms. The inference holds under the assumption of α-mixing without moment assumptions. As a result, the proposed tests are applicable to data from heavy-tailed or skewed distributions, including both continuous and ordered categorical responses. Simulation results and a real application confirm that the (mid-) rank procedures provide both robustness and increased power over the methods based on original observations for non-normally distributed data.

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Asymptotic distribution of rank statistics under dependencies with multivariate application

Cited by 28 publications

References 10 publications

Nonparametric Analysis of Ordered Categorical Data in Designs with Longitudinal Observations and Small Sample Sizes

Nonparametric Analysis of Ordered Categorical Data in Designs with Longitudinal Observations and Small Sample Sizes

Nonparametric methods for unbalanced multivariate data and many factor levels

Rank test for heteroscedastic functional data

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