On the information matrix of the multivariate skew-t model

SummaryThe multivariate skew-t distribution is currently under intense investigation because of several appealing properties. In this paper, we obtain the score vector of this distribution and we use it to study the behavior of the expected information matrix. We show in particular that this matrix is non-singular for finite values of the degree of freedom when the skewness vector is zero.

[1]  Marc G. Genton,et al.  Perturbation of Numerical Confidential Data via Skew-t Distributions , 2010, Manag. Sci..

[2]  Reinaldo Boris Arellano-Valle,et al.  Corrigendum to: "The centred parametrization for the multivariate skew-normal distribution" [J. Multivariate Analysis 99 (2008) 1362-1382] , 2009, J. Multivar. Anal..

[3]  M. Genton,et al.  Robust Likelihood Methods Based on the Skew‐t and Related Distributions , 2008 .

[4]  G. Zyskind.  Introduction to Matrices with Applications in Statistics , 1970 .

[5]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[6]  Ann F. S. Mitchell,et al.  The information matrix, skewness tensor and a-connections for the general multivariate elliptic distribution , 1989 .

[7]  M. Genton,et al.  A unified view on skewed distributions arising from selections , 2006 .

[8]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[9]  Jeremy MG Taylor,et al.  Robust Statistical Modeling Using the t Distribution , 1989 .

[10]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[11]  R. Arellano-Valle,et al.  The centred parametrization for the multivariate skew-normal distribution , 2008 .

[12]  Elliptical structural models , 1996 .

[13]  R. Arellano-Valle,et al.  On the Unification of Families of Skew‐normal Distributions , 2006 .

[14]  A. Azzalini,et al.  Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution , 2003, 0911.2342.

[15]  M. Genton,et al.  On fundamental skew distributions , 2005 .

[16]  D. Dey,et al.  A General Class of Multivariate Skew-Elliptical Distributions , 2001 .

[17]  A. Azzalini,et al.  Statistical applications of the multivariate skew normal distribution , 2009, 0911.2093.

[18]  Arjun K. Gupta.  Multivariate skew t-distribution , 2003 .