Differential geometry of Edgeworth expansions in curved exponential family

DOI10.1007/BF02480959zbMath0527.62034OpenAlexW1990198507WikidataQ115392122 ScholiaQ115392122MaRDI QIDQ595294

Shun-ichi Amari, Masayuki Kumon

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1007/bf02480959

zbMATH Keywords

Fisher informationEdgeworth expansionsmarginal distributionsconditional distributionscurved exponential familyancillary statisticsEfron curvaturehigher-order asymptotic theory

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic distribution theory in statistics (62E20) Local Riemannian geometry (53B20) Local differential geometry (53B99)

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Cites Work

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• Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference
• Local ancillarity
• Geometrical theory of asymptotic ancillarity and conditional inference
• Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information
• Note on N‐dimensional hermite polynomials
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