Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond

Statistical reasoning in dependent $p$-generalized elliptically contoured distributions and beyond. Subtitle: Testing scaling parameters, the role semi-inner products play, and simulating star-shaped distributed random vectors

First, likelihood ratio statistics for checking the hypothesis of equal variances of two-dimensional Gaussian vectors are derived both under the standard ( σ 2 1 , σ 2 2 , ) -parametrization and under the geometric (a, b,α)-parametrization where a2 and b2 are the variances of the principle components and α is an angle of rotation. Then, the likelihood ratio statistics for checking the hypothesi...

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

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...

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...

Tail dependence for elliptically contoured distributions