Search results for "M-estimator"

showing 3 items of 3 documents

On the Computation of Symmetrized M-Estimators of Scatter

2016

This paper focuses on the computational aspects of symmetrized Mestimators of scatter, i.e. the multivariate M-estimators of scatter computed on the pairwise differences of the data. Such estimators do not require a location estimate, and more importantly, they possess the important block and joint independence properties. These properties are needed, for example, when solving the independent component analysis problem. Classical and recently developed algorithms for computing the M-estimators and the symmetrized M-estimators are discussed. The effect of parallelization is considered as well as new computational approach based on using only a subset of pairwise differences. Efficiencies and…

Computer scienceComputation05 social sciencesEstimatorMultivariate normal distributionM-estimators01 natural sciencesIndependent component analysisscatter010104 statistics & probabilityScatter matrix0502 economics and businessPairwise comparison0101 mathematicsAlgorithmIndependence (probability theory)050205 econometrics Block (data storage)
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Symmetrised M-estimators of multivariate scatter

2007

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).

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