Statistics Papers
Title
Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process
Document Type
Journal Article
Date of this Version
3-1986
Publication Source
The Annals of Probability
Volume
14
Issue
1
Start Page
326
Last Page
335
DOI
10.1214/aop/1176992631
Abstract
An independent stationary process {Xi}∞i=1 in ℝn is perturbed by a sequence of Euclidean motions to obtain a new process {Yi}∞i=1. Criteria are given for the singularity or equivalence of these processes. When the distribution of the X process has finite Fisher information, the criteria are necessary and sufficient. Moreover, it is proved that it is exactly under the condition of finite Fisher information that the criteria are necessary and sufficient.
Copyright/Permission Statement
The original and published work is available at: https://projecteuclid.org/euclid.aop/1176992631#abstract
Keywords
Fisher information, Kakutani's product theorem, product measures, Euclidean motions, singular processes, Hellinger integrals
Recommended Citation
Steele, J. M. (1986). Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process. The Annals of Probability, 14 (1), 326-335. http://dx.doi.org/10.1214/aop/1176992631
Date Posted: 27 November 2017
This document has been peer reviewed.
Comments
At the time of publication, author J. Michael Steele was affiliated with Princeton University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.