On a class of extremal problems in statistics
- 1 January 1981
- journal article
- research article
- Published by Taylor & Francis in Mathematische Operationsforschung und Statistik. Series Optimization
- Vol. 12 (1) , 123-135
- https://doi.org/10.1080/02331938108842712
Abstract
Let m denote the infimum of the Integral of a function q w r t all probability measures with given marginals. The determination of m is of interest for a series of stochastic problems. In the present paper we prove a duality theorem for the determination of m and give some examples for its application. We consider especially the problem of extremal variance of sums of random variables and prove a theorem for the existence of random variables with given marginal distributions, such that their sum has variance zero.Keywords
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