Statistics Papers

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

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.

Keywords

Fisher information, Kakutani's product theorem, product measures, Euclidean motions, singular processes, Hellinger integrals

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Date Posted: 27 November 2017

This document has been peer reviewed.