Perez, A. “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. Cited in 3 Documents MSC: 62C99 Statistical decision theory 62B10 Statistical aspects of information-theoretic topics 62C05 General considerations in statistical decision theory 62B99 Sufficiency and information Keywords:set of probability measures; f-divergence; least favorable pair of; distributions; unfitted decision procedures; algorithm; barycenter concept; minimal-discrepancy estimating; discrimination rates PDF BibTeX XML