Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process
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Penn collection
Statistics Papers
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Fisher information
Kakutani's product theorem
product measures
Euclidean motions
singular processes
Hellinger integrals
Physical Sciences and Mathematics
Kakutani's product theorem
product measures
Euclidean motions
singular processes
Hellinger integrals
Physical Sciences and Mathematics
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Steele, J Michael
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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.
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1986-03-01
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The Annals of Probability
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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.