0000000000547659

AUTHOR

Thomas P. Hettmansperger

showing 3 related works from this author

Estimates of Regression Coefficients Based on the Sign Covariance Matrix

2002

SummaryA new estimator of the regression parameters is introduced in a multivariate multiple-regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the SCM regression estimate. The estimate is shown to be consistent with a limiting multinormal distribution. The influence function, as a function of the length of the contamination vector, is shown to be linea…

Statistics and ProbabilityEstimation of covariance matricesCovariance matrixLinear regressionStatisticsRegression analysisMultivariate normal distributionStatistics Probability and UncertaintyCovarianceAsymptotic theory (statistics)Least squaresMathematicsJournal of the Royal Statistical Society Series B: Statistical Methodology
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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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On the Efficiency of Affine Invariant Multivariate Rank Tests

1998

AbstractIn this paper the asymptotic Pitman efficiencies of the affine invariant multivariate analogues of the rank tests based on the generalized median of Oja are considered. Formulae for asymptotic relative efficiencies are found and, under multivariate normal and multivariatetdistributions, relative efficiencies with respect to Hotelling'sT2test are calculated.

CombinatoricsStatistics and ProbabilityMultivariate statisticsNumerical AnalysisRank (linear algebra)Consistent estimatorAffine invariantStatistics::MethodologyMultivariate normal distributionStatistics Probability and UncertaintyAsymptotic efficiency Oja median multivariate signed-rank test multivariate-rank test Pitman efficiencyMathematicsJournal of Multivariate Analysis
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