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October, 1989 Fisher Information and Dichotomies in Equivalence/Contiguity
Brian J. Thelen
Ann. Probab. 17(4): 1664-1690 (October, 1989). DOI: 10.1214/aop/1176991181


A contiguity dichotomy for two sequences of product measures is proved under the assumption of component measures belonging to a dominated experiment which is differentiable. This generalizes Eagleson's (1981) result for Gaussian measures. The dichotomy result is then used to generalize and clarify the results of Shepp (1965) and Steele (1986) with regards to finite Fisher information and equivalence dichotomies between two product measures, one with a fixed component measure and the second with rigidly perturbed component measures.


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Brian J. Thelen. "Fisher Information and Dichotomies in Equivalence/Contiguity." Ann. Probab. 17 (4) 1664 - 1690, October, 1989.


Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0688.62007
MathSciNet: MR1048953
Digital Object Identifier: 10.1214/aop/1176991181

Primary: 60G30
Secondary: 62F03

Keywords: Asymptotic separability , contiguity , dichotomy , equivalence , Fisher information , singularity

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 4 • October, 1989
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