0000000000640389

AUTHOR

David E. Tyler

showing 3 related works from this author

Asymptotic and bootstrap tests for subspace dimension

2022

Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li (2016). The eigen-decomposition of one scatter matrix with respect to another is then often used to determine the dimension of the signal subspace and to separate signal and noise parts of the data. Three popular dimension reduction methods, namely principal component analysis (PCA), fourth order blind identification (FOBI) and sliced inverse regression (SIR) are considered in detail and the first two moments of subsets of the eigenvalues are used to test…

FOS: Computer and information sciencesStatistics and ProbabilityPrincipal component analysisMathematics - Statistics TheoryStatistics Theory (math.ST)01 natural sciencesMethodology (stat.ME)010104 statistics & probabilityDimension (vector space)Scatter matrixSliced inverse regression0502 economics and businessFOS: MathematicsSliced inverse regressionApplied mathematics0101 mathematicsEigenvalues and eigenvectorsStatistics - Methodology050205 econometrics MathematicsestimointiNumerical AnalysisOrder determinationDimensionality reduction05 social sciencesriippumattomien komponenttien analyysimonimuuttujamenetelmätPrincipal component analysisStatistics Probability and UncertaintySubspace topologySignal subspace
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Tests and estimates of shape based on spatial signs and ranks

2009

Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance m…

Statistics and ProbabilityStatistics::TheoryRank (linear algebra)Covariance matrixNonparametric statisticsCovarianceEstimation of covariance matricesScatter matrixStatisticsStatistics::MethodologySign testStatistics Probability and Uncertaintymoniulotteiset merkki- ja jarjestysluvutMathematicsSign (mathematics)Journal of Nonparametric Statistics
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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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