Search results for "Matrix t-distribution"

showing 4 items of 4 documents

The asymptotic covariance matrix of the Oja median

2003

The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.

Statistics and ProbabilityCombinatoricsDelta methodMultivariate statisticsMatrix (mathematics)Multivariate analysis of varianceDimension (vector space)Matrix t-distributionApplied mathematicsEquivariant mapAffine transformationStatistics Probability and UncertaintyMathematicsStatistics & Probability Letters
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Inference based on the affine invariant multivariate Mann–Whitney–Wilcoxon statistic

2003

A new affine invariant multivariate analogue of the two-sample Mann–Whitney–Wilcoxon test based on the Oja criterion function is introduced. The associated affine equivariant estimate of shift, the multivariate Hodges-Lehmann estimate, is also considered. Asymptotic theory is developed to provide approximations for null distribution as well as for a sequence of contiguous alternatives to consider limiting efficiencies of the test and estimate. The theory is illustrated by an example. Hettmansperger et al. [9] considered alternative slightly different affine invariant extensions also based on the Oja criterion. The methods proposed in this paper are computationally more intensive, but surpri…

Statistics and ProbabilityDiscrete mathematicsMultivariate statisticsWilcoxon signed-rank testNull distributionMatrix t-distributionApplied mathematicsMultivariate normal distributionAffine transformationStatistics Probability and UncertaintyMathematicsNormal-Wishart distributionMultivariate stable distributionJournal of Nonparametric Statistics
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A matrix-valued Bernoulli distribution

2006

AbstractMatrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.

Statistics and ProbabilityNumerical AnalysisDISCRETEMODELSMatrix t-distributionMultivariate normal distributionMatrix-valued distributionsBINARYNormal-Wishart distributionBinomial distributionBernoulli distributionCategorical distributionStatisticsApplied mathematicsBernoulli processStatistics Probability and UncertaintyCorrelated multivariate binary responsesMathematicsMultivariate stable distributionMultivariate Bernoulli distributionJournal of Multivariate Analysis
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Affine equivariant multivariate rank methods

2003

The classical multivariate statistical methods (MANOVA, principal component analysis, multivariate multiple regression, canonical correlation, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations. In the paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. Affine equivariant multivariate rank concept is based on the multivariate Oja (Statist. Probab. …

Statistics and ProbabilityPure mathematicsApplied MathematicsMatrix t-distributionMultivariate normal distributionNormal-Wishart distributionCombinatoricsEstimation of covariance matricesScatter matrixStatistics::MethodologyMatrix normal distributionMultivariate t-distributionStatistics Probability and UncertaintyMathematicsMultivariate stable distributionJournal of Statistical Planning and Inference
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