Afrika Statistika

Process of random distributions classification and prediction

Richard Emilion

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Abstract

We define a continuous time stochastic process such that each is a Ferguson-Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case.

We give an application in classifiying moving distributions by proving that the above random distributions are generally mutually orthogonal. The proofs hinge on a theorem of Kakutani.

Article information

Source
Afr. Stat., Volume 1, Number 1 (2005), 27-46.

Dates
Received: 1 February 2005
First available in Project Euclid: 26 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1495762651

Digital Object Identifier
doi:10.4314/afst.v1i1.46871

Mathematical Reviews number (MathSciNet)
MR2298873

Subjects
Primary: 60G07: General theory of processes
Secondary: 60G57: Random measures 62F10: Point estimation 62G05: Estimation

Keywords
Bayesian Clustering Dirichlet distributions Dirichlet processes E.M. algorithm gamma processes Kraft processes nonparametric estimation random distributions S.A.E.M. algorithm weighted gamma processes

Citation

Emilion, Richard. Process of random distributions classification and prediction. Afr. Stat. 1 (2005), no. 1, 27--46. doi:10.4314/afst.v1i1.46871. https://projecteuclid.org/euclid.as/1495762651


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