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Hellinger integrals, contiguity and entire separation. (English) Zbl 0638.60001

Let P, Q and R be three probability measures on some probability measure space such that R dominates both P and Q. Let X and Y be Radon-Nikodym derivatives of P and Q w.r.t. R. Then the integrals \(\int_{A}X\) s \(Y^{1-s} dR\) and \(\int X\) s \(Y^{1-s} dR\), where \(0<s<1\) and A is an event, define respectively a Hellinger measure and a Hellinger integral of order s.
Hellinger integrals of distribution laws are estimated in terms of Hellinger integrals of the corresponding conditional distributions belonging to an increasing sequence of sub-sigma-algebras. These estimates are then employed to derive necessary and sufficient conditions for contiguity and entire separation of two sequences of probability measures.
Reviewer: A.Mukherjea

MSC:

60A10 Probabilistic measure theory
60E99 Distribution theory
62B99 Sufficiency and information
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References:

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