Measure of information and contiguity

Madan Lal Puri and István Vincze

Statistics & Probability Letters, 1990, vol. 9, issue 3, 223-228

Abstract: A characterization of contiguity was provided by Oosterhoff and van Zwet (1979) by means of the Hellinger distance and also by using a condition involving the tail probabilities. Independence of the observations involved, under both sequences of measures, was also part of the assumptions made. The aim of the present paper is to give a characterization of mutual contiguity based solely on an information (distance) quantity and valid for any pair of sequences of measures indexed by a parameter n of arbitrary nature, tending to a certain limit (say, n[infinity]). A further parameter Nn is a nonnegative number tending to infinity when n tends to n[infinity]. For the sake of simplicity, both n and Nn will be assumed to be nonnegative integers. The random variables involved are not assumed to be independent. The authors of this note intend to discuss some applications of the results obtained here in a forthcoming report.

Date: 1990
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