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January, 1986 Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process
J. Michael Steele
Ann. Probab. 14(1): 326-335 (January, 1986). DOI: 10.1214/aop/1176992631

Abstract

An independent stationary process $\{X_i\}^\infty_{i=1}$ in $\mathbb{R}^n$ is perturbed by a sequence of Euclidean motions to obtain a new process $\{Y_i\}^\infty_{i=1}$. 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.

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J. Michael Steele. "Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process." Ann. Probab. 14 (1) 326 - 335, January, 1986. https://doi.org/10.1214/aop/1176992631

Information

Published: January, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0592.60033
MathSciNet: MR815974
Digital Object Identifier: 10.1214/aop/1176992631

Subjects:
Primary: 60G30
Secondary: 60B15

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

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 1 • January, 1986
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