Amari, Shun-ichi Differential geometry of curved exponential families. Curvatures and information loss. (English) Zbl 0507.62026 Ann. Stat. 10, 357-385 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 ReviewsCited in 99 Documents MSC: 62F12 Asymptotic properties of parametric estimators 62E20 Asymptotic distribution theory in statistics 62B10 Statistical aspects of information-theoretic topics 53B05 Linear and affine connections 53A99 Classical differential geometry Keywords:curved exponential families; multi-parameter families of distributions; Legendre transformation; second-order information loss; Fisher-efficient estimators; maximum-likelihood estimator; statistical curvatures; statistical affine connections; recovery of information; duality; second- order efficiency; Kullback-Leibler distance PDF BibTeX XML Cite \textit{S.-i. Amari}, Ann. Stat. 10, 357--385 (1982; Zbl 0507.62026) Full Text: DOI