Amari, S. Theory of information spaces: A differential-geometrical foundation of statistics. Geometrical theory of asymptotic ancillarity and conditional inference.
Stanford's star of statistical inference: a Q&A with Bradley Efron | StatsLife
Biometrika, 69 , 1— Differential geometry of curved exponential families — curvatures and information loss. Differential geometry of Edgeworth expansions in curved exponential family.
Chibisov, D. An asymptotic expansion for a class of estimators containing maximum likelihood estimators.
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Differential geometry in statistical inference
Efron, B. Defining the curvature of a statistical problem with application to second order efficiency with Discussions.
Ghosh, J. Second-order efficiency of maximum likelihood estimators.
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Kumon, M. Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference. Biometrika, , to appear. Nagaoka, H. Differential geometry of smooth families of probability distributions.
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Statistical inference under multiterminal rate restrictions: a differential geometric approach Abstract: A statistical inference problem for a two-terminal information source emitting mutually correlated signals X and Y is treated. This compression causes a loss of the statistical information available for testing hypotheses concerning X and Y.
It is shown that the differential geometry of the manifold of all probability distributions plays a fundamental role in this type of multiterminal problem connecting Shannon information and statistical information. A brief introduction to the dually coupled e-affine and m-affine connections together with e-flatness and m-flatness is given. Article :.
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