6533b827fe1ef96bd12870f3

RESEARCH PRODUCT

Symmetrised M-estimators of multivariate scatter

Sara TaskinenSeija SirkiäHannu Oja

subject

Statistics and ProbabilityElliptical distributionInfluence functionMultivariate statisticsNumerical AnalysisEstimatorEfficiencyM-estimatorM-estimatorIndependent component analysisEfficient estimatorScatter matrixScatter matrixMathematics::Category TheoryStatisticsApplied mathematicsStatistics Probability and UncertaintyRobustnessElliptical distributionIndependence (probability theory)Mathematics

description

AbstractIn this paper we introduce a family of symmetrised M-estimators of multivariate scatter. These are defined to be M-estimators only computed on pairwise differences of the observed multivariate data. Symmetrised Huber's M-estimator and Dümbgen's estimator serve as our examples. The influence functions of the symmetrised M-functionals are derived and the limiting distributions of the estimators are discussed in the multivariate elliptical case to consider the robustness and efficiency properties of estimators. The symmetrised M-estimators have the important independence property; they can therefore be used to find the independent components in the independent component analysis (ICA).

yearjournalcountryeditionlanguage
2007-09-01Journal of Multivariate Analysis
10.1016/j.jmva.2007.06.005http://dx.doi.org/10.1016/j.jmva.2007.06.005