Nonparametric methods for unbalanced multivariate data and many factor levels

Solomon W. Harrar; Arne C. Bathke

doi:10.1016/j.jmva.2008.01.005

Nonparametric methods for unbalanced multivariate data and many factor levels

Solomon W. Harrar, Arne C. Bathke

Dr. Bing Zhang Department of Statistics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1635-1664
Number of pages	30
Journal	Journal of Multivariate Analysis
Volume	99
Issue number	8
DOIs	https://doi.org/10.1016/j.jmva.2008.01.005
State	Published - Sep 2008

Keywords

62G10
62G20
62H10
62H15
62J10
Multivariate analysis of variance
Nonnormality
Nonparametric model
Ordinal data
Rank statistic
Unbalanced design

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2008.01.005

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abstract = "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 ni 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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KW - 62H15

KW - 62J10

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KW - Nonnormality

KW - Nonparametric model

KW - Ordinal data

KW - Rank statistic

KW - Unbalanced design

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JO - Journal of Multivariate Analysis

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ER -

Nonparametric methods for unbalanced multivariate data and many factor levels

Abstract

Keywords

ASJC Scopus subject areas

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