Statistical morphisms and related invariance properties

DOI10.1007/BF00048669zbMath0782.62013OpenAlexW1999857050MaRDI QIDQ1206630

Dominique Picard

Publication date: 1 April 1993

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00048669

zbMATH Keywords

entropymetricRiemannian manifoldconnectionsinvariance propertiesmorphismsflat manifoldspower functionstatistical manifoldcomparison of experimentsGaussian experimentsAmari connectionscontiguous neighborhoodentropy invarianceexperiment invariancelikelihood expansionslocal invariance of selected orderMarkov morphismsNeymann Pearson testnonflat manifoldspair of dual torsion free connectionsstatistical morphisms

Mathematics Subject Classification ID

Theory of statistical experiments (62B15) Asymptotic properties of parametric tests (62F05) Local differential geometry (53B99)

Cites Work

• Differential geometry of Edgeworth expansions in curved exponential family
• Differential geometry, profile likelihood, L-sufficiency and composite transformation models
• Second order efficiency of minimum contrast estimators in a curved exponential family
• Asymptotic efficiency of statistical estimators: concepts and higher order asymptotic efficiency
• Defining the curvature of a statistical problem (with applications to second order efficiency)
• Differential geometry of curved exponential families. Curvatures and information loss
• Differential-geometrical methods in statistics
• The Role of Differential Geometry in Statistical Theory
• Comparison of experiments when the parameter space is finite
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