On the Fisher Information Matrix for Multivariate Elliptically Contoured Distributions

Elliptically Contoured Distributions

Given two covar iance matrices R and S for a given elliptically con toured distribution, we show how simple inequalities between the matr ix elements imply that ER(f)< Es(f), e.g., when x = (xil,i ...... i,) is a mult i index vector and f ( x ) = rain max rain max. . .xi l ..... i,, i l i2 i3 or f(x) is the indicator funct ion of sets such as (3 U N U...rx, ...... ~._-<;o, ..... ,~ i l i2 i3

Multivariate elliptically contoured stable distributions: theory and estimation

Mulitvariate stable distributions with elliptical contours are a class of heavy tailed distributions that can be useful for modeling financial data. This paper describes the theory of such distributions, presents formulas for calculating their densities, methods for fitting the data and assessing the fit. Numerical routines are described that work for dimension d ≤ 40. An example looks at a por...

On the Theory of Elliptically Contoured Distributions

The theory of elliptically contoured distributions is presented in an unrestricted setting (without reference to moment restrictions or assumptions of absolute continuity). These distributions are defined parametrically through their characteristic functions, and then studied primarily through the use of stochastic representations which naturally follow from the seminal work of Schoenberg on sp...

A Note on Hilbertian Elliptically Contoured Distributions

In this paper, we discuss elliptically contoured distribution for random variables defined on a separable Hilbert space. It is a generalization of the multivariate elliptically contoured distribution to distributions on infinite dimensional spaces. Some theoretical properties of the Hilbertian elliptically contoured distribution are discussed, examples on functional data are investigated to ill...

Tail dependence for elliptically contoured distributions