High-dimensional star-shaped distributions

Abstract

Stochastic representations of star-shaped distributed random vectors having heavy or light tail density generating function g are studied for increasing dimensions along with corresponding geometric measure representations. Intervals are considered where star radius variables take values with high probability, and the derivation of values of distribution functions of g-robust statistics is proved to be based upon considering random events whose probability is asymptotically negligible if the dimension of the sample vector is approaching infinity. Moreover, a principal component representation of p-generalized elliptically contoured p-generalized Gaussian distributions is discussed.