Chentsov, N. N. Statistical decision rules and optimal inference. Transl. from the Russian by the Israel Program for Scientific Translations; ed. by Lev J. Leifman. (English) Zbl 0484.62008 Translations of Mathematical Monographs, 53. Providence, R.I.: American Mathematical Society (AMS). VIII, 499 p. $ 76.00 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 10 ReviewsCited in 95 Documents MSC: 62C05 General considerations in statistical decision theory 62-02 Research exposition (monographs, survey articles) pertaining to statistics 18F99 Categories in geometry and topology 62A01 Foundations and philosophical topics in statistics 53B99 Local differential geometry 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C99 Global differential geometry 53B20 Local Riemannian geometry Keywords:category of statistical decision rules; Klein geometry of sets of probability distributions; dominated families of distributions; Markov morphisms; invariants; Kullback-Leibler information; equivariant infinitesimal geometries; invariant Euclidean metrics; manifold of probability distributions; information inequality; exponential families PDFBibTeX XML