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Amari, Shun-ichi

Differential geometry of curved exponential families. Curvatures and information loss. (English) Zbl 0507.62026

Ann. Stat. 10, 357-385 (1982).
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scan of Zbl 0507.62026

Cited in 12 Reviews
Cited in 120 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
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