المؤلفون: Dürre, Alexander¹ alexander.duerre@udo.edu, Tyler, David E.², Vogel, Daniel³

المصدر: Statistics & Probability Letters. Apr2016, Vol. 111, p80-85. 6p.

مصطلحات موضوعية: *EIGENVALUES, *ANALYSIS of covariance, *MATRICES (Mathematics), *MATHEMATICAL functions, *COMPUTATIONAL complexity

مستخلص: We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation. [ABSTRACT FROM AUTHOR]

المؤلفون: Chen, Zhiqiang¹ chenz@wpunj.edu, Tyler, David E.² dtyler@rci.rutgers.edu

المصدر: Journal of Statistical Planning & Inference. May2004, Vol. 122 Issue 1/2, p111. 14p.

مصطلحات موضوعية: *MULTIVARIATE analysis, *MEDIAN (Mathematics), *ROBUST statistics, *MATHEMATICAL statistics

مستخلص: Some curious properties of Tukey''s depth and Tukey''s multivariate median are revealed by examining their behavior at multivariate distributions possessing independent and identically distributed symmetric stable marginals. In particular, (i) the shape of the contours for Tukey''s depth can be the same for large classes of distributions, (ii) the influence function of a linear combination of the components of Tukey''s median can be uniformly smaller than the influence function of the univariate median for the corresponding linear combination of the multivariate distribution, and (iii) the maximum bias under epsilon contamination for Tukey''s median can be smaller than the maximum bias of the median of some univariate projections of the data. [Copyright &y& Elsevier]

المؤلفون: Tyler, David E.¹ dtyler@rci.rutgers.edu

المصدر: Statistics & Probability Letters. Sep2010, Vol. 80 Issue 17/18, p1409-1413. 5p.

مصطلحات موضوعية: *MULTIVARIATE analysis, *SCATTERING (Mathematics), *STATISTICS, *MATRICES (Mathematics), *ANALYSIS of covariance, *MATHEMATICAL constants, *DEPENDENCE (Statistics)

مستخلص: Abstract: For a -dimensional data set of size in general position, it is shown that the only affine equivariant multivariate location statistic is the sample mean vector and that any affine equivariant scatter matrix must be proportional to the sample covariance matrix, with the proportionality constant not being dependent on the data. [Copyright &y& Elsevier]

المؤلفون: Fernholz, Luisa Turrin¹, Tyler, David E.², Yohai, Victor³

المصدر: Journal of Statistical Planning & Inference. May2004, Vol. 122 Issue 1/2, p1. 2p.