6533b7d3fe1ef96bd1260aa7
RESEARCH PRODUCT
Multivariate nonparametric tests in a randomized complete block design
Jürg HüslerJ. MöttönenHannu Ojasubject
Multivariate Friedman testStatistics and ProbabilityMultivariate statisticsNumerical AnalysisMultivariate analysisUnivariateNonparametric statisticsMultivariate normal distributionPitman efficiencyRotation invarianceMultivariate analysis of varianceFriedman testAffine invarianceStatisticsTest statisticSpatial rankStatistics Probability and UncertaintyMultivariate Page testMathematicsdescription
AbstractIn this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the multivariate normal and t distribution cases. The tests are rotation invariant only, but affine invariant versions can be easily constructed. The theory is illustrated by an example.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-04-01 | Journal of Multivariate Analysis |