Search results for "Spatial rank"

showing 3 items of 3 documents

Multivariate nonparametric tests in a randomized complete block design

2003

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 Friedman testStatistics and ProbabilityMultivariate statisticsNumerical AnalysisMultivariate analysisUnivariateNonparametric statisticsMultivariate normal distributionPitman efficiencyRotation invarianceMultivariate analysis of varianceFriedman testAffine invarianceStatisticsTest statisticSpatial rankStatistics Probability and UncertaintyMultivariate Page testMathematicsJournal of Multivariate Analysis
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k-Step shape estimators based on spatial signs and ranks

2010

In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in Dümbgen (1998) and Oja and Randles (2004) and further studied for example in Sirkiä et al. (2009). The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the es…

Statistics and ProbabilityInfluence functionCovariance matrixApplied MathematicsAffiinisti ekvivarianttitehokkuusspatiaalinen järjestyslukuEstimatorSpatial signEfficiencyM-estimatorEfficient estimatorinfluenssifunktioExtremum estimatorHeavy-tailed distributionStatisticsAffine equivarianceStatistics Probability and UncertaintySpatial rankInvariant estimatorIndependence (probability theory)Mathematicsspatiaalinen merkki
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Multivariate Nonparametric Tests

2004

Multivariate nonparametric statistical tests of hypotheses are described for the one-sample location problem, the several-sample location problem and the problem of testing independence between pairs of vectors. These methods are based on affine-invariant spatial sign and spatial rank vectors. They provide affine-invariant multivariate generalizations of the univariate sign test, signed-rank test, Wilcoxon rank sum test, Kruskal–Wallis test, and the Kendall and Spearman correlation tests. While the emphasis is on tests of hypotheses, certain references to associated affine-equivariant estimators are included. Pitman asymptotic efficiencies demonstrate the excellent performance of these meth…

Statistics and Probabilityeducation.field_of_studyMultivariate statisticsspatial signWilcoxon signed-rank testGeneral MathematicsRank (computer programming)PopulationNonparametric statisticsUnivariaterobustnessSpearman's rank correlation coefficientspatial rankPitman efficiencyStatisticsAffine invarianceEconometricsSign testStatistics::MethodologyStatistics Probability and UncertaintyeducationMathematics
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