scholarly journals EXTENSION OF THE OLKIN AND RUBIN CHARACTERIZATION TO THE WISHART DISTRIBUTION ON HOMOGENEOUS CONES

2011 ◽  
Vol 14 (04) ◽  
pp. 591-611 ◽  
Author(s):  
I. BOUTOURIA ◽  
A. HASSAIRI ◽  
H. MASSAM
Keyword(s):  
Wishart Distribution ◽  
Symmetric Cone ◽  
Symmetric Matrices ◽  
Riesz Distribution ◽  
Homogeneous Cones ◽  
Homogeneous Cone

The Wishart distribution on a homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the ordinary Wishart distribution on symmetric matrices.

scholarly journals Further generalization of symmetric multiplicity theory to the geometric case over a field

2021 ◽  
Vol 9 (1) ◽  
pp. 31-35
Author(s):  
Isaac Cinzori ◽  
Charles R. Johnson ◽  
Hannah Lang ◽  
Carlos M. Saiago
Keyword(s):  
Symmetric Matrices

Abstract Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

A characterization of complex homogeneous cones

1980 ◽  
Vol 170 (2) ◽  
pp. 181-194 ◽  
Author(s):  
Alan T. Huckleberry ◽  
Eberhard Oeljeklaus
Keyword(s):  
Homogeneous Cones

scholarly journals The multiparameter t’distribution

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4137-4150 ◽  
Author(s):  
Emna Ghorbel ◽  
Mahdi Louati
Keyword(s):  
Mean Squared Error ◽  
Natural Extension ◽  
Expectation Maximization Algorithm ◽  
Infinite Divisibility ◽  
Cholesky Decomposition ◽  
Wishart Distribution ◽  
Normal Vector ◽  
Riesz Distribution ◽  
Estimated Parameters ◽  
T Distribution

This research paper stands for an extension to the multivariate t?distribution introduced in 1954 by Cornish, Dunnett and Sobel, namely the multiparameter t?distribution. This distribution is expressed in two different ways. The first way invests the mixture of a normal vector with a natural extension to the Wishart distribution, that is the Riesz distribution on symmetric matrices. The second one rests upon the Cholesky decomposition of the Riesz matrix. An algorithm for generating this distribution is investigated using the Riesz distribution arising obtained through not only the distribution of the empirical normal covariance matrix for samples with monotone missing data but also through Cholesky decomposition. In addition, Some fundamentals properties of the multiparameter t?distribution such as the infinite divisibility are identified. Besides, the Expectation Maximization algorithm is used to estimate its parameters. Finally, the performance of these estimators is assessed by means of the Mean Squared Error between the true and the estimated parameters.

scholarly journals Characterization of the Riesz exponential family on homogeneous cones

2019 ◽  
Vol 158 (1) ◽  
pp. 45-57 ◽  
Author(s):  
Hideyuki Ishi ◽  
Bartosz Kołodziejek
Keyword(s):  
Exponential Family ◽  
Homogeneous Cones

scholarly journals Functions Preserving Orthogonality of Hermitian Matrices

2021 ◽  
Vol 13 (4) ◽  
pp. 77
Author(s):  
Meili Liu ◽  
Liwei Wang ◽  
Chun-Te Lee ◽  
Jeng-Eng Lin
Keyword(s):  
Symmetric Matrices ◽  
Hermitian Matrices ◽  
Orthogonal Matrices ◽  
Triangular Matrices ◽  
Upper Triangular Matrices

Inspired by the results that functions preserve orthogonality of full matrices, upper triangular matrices, and symmetric matrices. We finish the work by finding special orthogonal matrices which satisfy the conditions of preserving orthogonality functions. We give a characterization of functions preserving orthogonality of Hermitian matrices.

A Computable Characterization of the Extrinsic Mean of Reflection Shapes and Its Asymptotic Properties

2015 ◽  
Vol 32 (01) ◽  
pp. 1540005
Author(s):  
Chao Ding ◽  
Hou-Duo Qi
Keyword(s):  
Hypothesis Test ◽  
Asymptotic Properties ◽  
Shape Space ◽  
Direct Application ◽  
Symmetric Matrices ◽  
Geometric Information ◽  
Computable Formula ◽  
Arbitrary Dimensions ◽  
Extrinsic Mean

The reflection shapes of configurations in ℜm with k landmarks consist of all the geometric information that is invariant under compositions of similarity and reflection transformations. By considering the corresponding Schoenberg embedding, we embed the reflection shape space into the Euclidean space of all (k - 1) by (k - 1) real symmetric matrices. In this paper, we provide a computable formula of the extrinsic mean of the reflection shapes in arbitrary dimensions. Moreover, the asymptotic analysis of the extrinsic mean of the reflection shapes is studied. By using the differentiability of spectral operators, we obtain a central limit theorem of the sample extrinsic mean of the reflection shapes. As a direct application, the two-example hypothesis test of the reflection shapes is also derived.

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