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Best approximations to random variables based on trimming procedures. (English) Zbl 0745.41030

This paper deals with obtaining best approximation to random variables based on trimming procedures which both do not depend on arbitrary decisions and can be defined directly for \(R^ n\)-valued r.v. For a class of suitable nondecreasing functions a family of best approximations to an \(R^ n\)-valued random variable based on trimming procedures is obtained. Existence and a characterization which relates the best approximations and the best trimming sets are obtained. The problem of uniqueness is studied for real valued random variables.
Reviewer: K.Najzar (Praha)

MSC:

41A50 Best approximation, Chebyshev systems
60A99 Foundations of probability theory
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