Free Exponential Families as Kernel Families
Probability
2010-06-08 v4 Operator Algebras
Statistics Theory
Statistics Theory
Abstract
Free exponential families have been previously introduced as a special case of the q-exponential family. We show that free exponential families arise also from a procedure analogous to the definition of exponential families by using the Cauchy-Stieltjes kernel instead of the exponential kernel. We use this approach to re-derive several known results and to study further similarities with exponential families and reproductive exponential models.
Cite
@article{arxiv.math/0601273,
title = {Free Exponential Families as Kernel Families},
author = {Wlodzimierz Bryc},
journal= {arXiv preprint arXiv:math/0601273},
year = {2010}
}
Comments
Major revision; same theorems in different layout. 12 pages