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“Barycenter” of a set of probability measures and its application in statistical decision. (English) Zbl 0577.62011
Computational statistics, Proc. 6th Symp., Prague 1984, 154-159 (1984).
Summary: [For the entire collection see Zbl 0559.00009.]
After introducing the concept of ”barycenter” of a set $${\mathcal S}$$ of probability measures as a probability measure from a given projection family minimizing its maximal discrepancy with respect to the probability measures of the set $${\mathcal S}$$, we give an algorithm for constructing the barycenter in some important cases.
The barycenter concept plays an important role in statistical decision, namely in minimal-discrepancy estimating and its improvement if more estimates are available, in determining discrimination rates and LFP of distributions in hypothesis testing, in approximating a multidimensional distribution by a set of its marginals.

##### MSC:
 62C99 Statistical decision theory 62B10 Statistical aspects of information-theoretic topics 62C05 General considerations in statistical decision theory 62B99 Sufficiency and information