Search results for "Law of total covariance"

showing 3 items of 3 documents

The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies

2003

We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform …

Statistics and ProbabilityCovariance functionaffine equivarianceinfluence functionMultivariate normal distributionrobustnessComputer Science::Human-Computer InteractionEfficiencyestimatorsEstimation of covariance matricesScatter matrixStatisticsAffine equivarianceApplied mathematicsCMA-ESMultivariate signCovariance and correlation matricesRobustnessmultivariate medianMathematicsprincipal componentsInfluence functionNumerical AnalysisMultivariate medianCovariance matrixcovariance and correlation matricesdiscriminant-analysisCovarianceComputer Science::Otherdispersion matricesefficiencyLaw of total covariancemultivariate locationtestsStatistics Probability and Uncertaintyeigenvectors and eigenvaluesEigenvectors and eigenvaluesmultivariate signJournal of Multivariate Analysis
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Linear Recursive Equations, Covariance Selection, and Path Analysis

1980

Abstract By defining a reducible zero pattern and by using the concept of multiplicative models, we relate linear recursive equations that have been introduced by econometrician Herman Wold (1954) and path analysis as it was proposed by geneticist Sewall Wright (1923) to the statistical theory of covariance selection formulated by Arthur Dempster (1972). We show that a reducible zero pattern is the condition under which parameters as well as least squares estimates in recursive equations are one-to-one transformations of parameters and of maximum likelihood estimates, respectively, in a decomposable covariance selection model. As a consequence, (a) we can give a closed-form expression for t…

Statistics and ProbabilityMathematical optimizationEstimation of covariance matricesCovariance functionCovariance matrixLaw of total covarianceApplied mathematicsRational quadratic covariance functionCovariance intersectionStatistics Probability and UncertaintyCovarianceStatistical theoryMathematicsJournal of the American Statistical Association
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Robustifying principal component analysis with spatial sign vectors

2012

Abstract 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.

Statistics and ProbabilityMathematical optimizationEstimation of covariance matricesMatérn covariance functionCovariance functionCovariance matrixLaw of total covarianceApplied mathematicsRational quadratic covariance functionCovariance intersectionStatistics Probability and UncertaintyCovarianceMathematicsStatistics & Probability Letters
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