Diagnostic Procedures for Spherically Symmetric Distributions

Springer Proceedings in Mathematics & Statistics - Topics in Nonparametric Statistics ◽

10.1007/978-1-4939-0569-0_16 ◽

2014 ◽

pp. 177-183

Author(s):

Simos G. Meintanis

Keyword(s):

Diagnostic Procedures ◽

Spherically Symmetric ◽

Symmetric Distributions

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Minimax estimators that shift towards a hypersphere for location vectors of spherically symmetric distributions

Journal of Multivariate Analysis ◽

10.1016/0047-259x(85)90075-2 ◽

1985 ◽

Vol 17 (2) ◽

pp. 127-147 ◽

Cited By ~ 13

Author(s):

M.E Bock

Keyword(s):

Spherically Symmetric ◽

Symmetric Distributions ◽

Minimax Estimators

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Marginal Replacement in Multivariate Densities, with Application to Skewing Spherically Symmetric Distributions

Journal of Multivariate Analysis ◽

10.1006/jmva.2001.1993 ◽

2002 ◽

Vol 81 (1) ◽

pp. 85-99 ◽

Cited By ~ 22

Author(s):

M.C. Jones

Keyword(s):

Spherically Symmetric ◽

Symmetric Distributions

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Spline approximations to spherically symmetric distributions

Numerische Mathematik ◽

10.1007/bf01389619 ◽

1986 ◽

Vol 49 (2-3) ◽

pp. 111-121 ◽

Cited By ~ 17

Author(s):

Walter Gautschi ◽

Gradimir V. Milovanović

Keyword(s):

Spherically Symmetric ◽

Symmetric Distributions

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Minimax estimation of the mean of spherically symmetric distributions under general quadratic loss

Journal of Multivariate Analysis ◽

10.1016/0047-259x(79)90059-9 ◽

1979 ◽

Vol 9 (4) ◽

pp. 579-588 ◽

Cited By ~ 25

Author(s):

Ann Cohen Brandwein

Keyword(s):

Minimax Estimation ◽

Quadratic Loss ◽

Spherically Symmetric ◽

Symmetric Distributions ◽

The Mean

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On some classes of spherically symmetric distributions

Journal of Soviet Mathematics ◽

10.1007/bf01099016 ◽

1991 ◽

Vol 57 (4) ◽

pp. 3189-3192

Author(s):

N. A. Volodin

Keyword(s):

Spherically Symmetric ◽

Symmetric Distributions

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Spherically Symmetric Distributions

Robustness of Statistical Tests ◽

10.1016/b978-0-12-398230-8.50006-6 ◽

1989 ◽

pp. 1-14

Author(s):

Takeaki Kariya ◽

Bimal K. Sinha

Keyword(s):

Spherically Symmetric ◽

Symmetric Distributions

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On principal points for location mixtures of spherically symmetric distributions

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2005.11.010 ◽

2008 ◽

Vol 138 (11) ◽

pp. 3405-3418 ◽

Cited By ~ 15

Author(s):

Hiroshi Kurata

Keyword(s):

Spherically Symmetric ◽

Symmetric Distributions ◽

Principal Points

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A Class of Spherical and Elliptical Distributions with Gaussian-Like Limit Properties

Journal of Probability and Statistics ◽

10.1155/2012/467187 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 2

Author(s):

Chris Sherlock ◽

Daniel Elton

Keyword(s):

Functional Form ◽

Marginal Distribution ◽

Random Variables ◽

Spherically Symmetric ◽

Sufficient Condition ◽

Elliptical Distributions ◽

Symmetric Distributions ◽

One Dimensional ◽

Elliptically Symmetric Distributions

We present a class of spherically symmetric random variables defined by the property that as dimension increases to infinity the mass becomes concentrated in a hyperspherical shell, the width of which is negligible compared to its radius. We provide a sufficient condition for this property in terms of the functional form of the density and then show that the property carries through to equivalent elliptically symmetric distributions, provided that the contours are not too eccentric, in a sense which we make precise. Individual components of such distributions possess a number of appealing Gaussian-like limit properties, in particular that the limiting one-dimensional marginal distribution along any component is Gaussian.

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