Search results for "Spatial sign"

showing 3 items of 3 documents

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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Robustifying principal component analysis with spatial sign vectors

2012

In this paper, we apply orthogonally equivariant spatial sign covariance matrices as well as their affine equivariant counterparts in principal component analysis. The influence functions and asymptotic covariance matrices of eigenvectors based on robust covariance estimators are derived in order to compare the robustness and efficiency properties. We show in particular that the estimators that use pairwise differences of the observed data have very good efficiency properties, providing practical robust alternatives to classical sample covariance matrix based methods. peerReviewed

robustisuusvaikutusfunktiospatiaalinen merkkivektoriefficiencyinfluence functionAffiinisti ekvivarianttisuustehokkuusAffine equivariancerobustnessspatial sign vector
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