Re: Regression via PI in One-Sided Direction
From: Osher Doctorow (mdoctorow_at_comcast.net)
Date: 10/26/04
- Next message: Russell Martin: "Re: "Sphere the data""
- Previous message: Batu Chalise: "weighted sum of independent beta random variables"
- In reply to: Osher Doctorow: "Re: Regression via PI in One-Sided Direction"
- Messages sorted by: [ date ] [ thread ]
Date: Tue, 26 Oct 2004 16:51:31 +0000 (UTC)
On 26 Oct 04 02:24:43 -0400 (EDT), Osher Doctorow wrote:
>I should mention at this point the paper of C. Donati-Martin of
>Laboratoire de Probabilites et Modeles Aleatoires, U. Paris, "Large
>deviations for Wishart processes," arXiv:math.PR/0410457 v1 21 Oct
>2004, who applies a Riccati differential equation (matrix form) to
>obtain a Large Deviations bound for the largest eigenvalue of a
The Wishart distribution and Wishart process are especially interest-
ing from the viewpoint of PI because they are an "almost generaliza-
tion" of the chi-square distribution which is a special case of
the gamma distributions. They are not usually considered to be an
exact generalization because the off-diagonal elements (unlike the
diagonal elements) aren't distributed chi-square. The gamma
distribution is PI-optimal for one known and one unknown parameter,
while its special case the exponential distribution is Shannon
maximum entropy (continuous) optimal. Wishart is important in
maximum likelihood estimation (MLE) for multivariate normal distribu-
tions and has additivity "reproductive" properties somewhat similar
to the normal and chi-square distributions although it is multivar-
iate. They have interesting relationships to theory of non-colliding
versus colliding (eigenvalue) processes and squared Bessel processes.
Another interesting paper is by C. Donati-Martin et al (2003), which
is accessible under the keywords: "DC metadata pour: Some properties
of the Wishart processes and a matrix extension of the Hartman-
Watson laws," on the internet (from U. de Paris), which also has
highlights of the rather "inaccessible" 1991 paper by Bru at least
for non-subscribers on the internet.
Osher Doctorow
- Next message: Russell Martin: "Re: "Sphere the data""
- Previous message: Batu Chalise: "weighted sum of independent beta random variables"
- In reply to: Osher Doctorow: "Re: Regression via PI in One-Sided Direction"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
