Titlebook: Differential-Geometrical Methods in Statistics; Shun-ichi Amari Book 1985 Springer-Verlag Berlin Heidelberg 1985 Estimator.probability.pro

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Reasons for Action — Second Parterest. We next study the amount of information loss caused by not knowing the true value of the nuisance parameter. It is related to the mixture curvature of the submanifold defined by the nuisance parameter.

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Information, Ancillarity and Conditional Inference statistics one should condition when there are a number of ancillaries. Finally, the sufficient vector statistic x is decomposed into component statistics of geometrical character according as the magnitude of the amount of information.

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Statistical Inference in the Presence of Nuisance Parameterserest. We next study the amount of information loss caused by not knowing the true value of the nuisance parameter. It is related to the mixture curvature of the submanifold defined by the nuisance parameter.

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0930-0325 ng the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #.Manuscripta Geodaetica.#2978-0-387-96056-2978-1-4612-5056-2Series ISSN 0930-0325 Series E-ISSN 2197-7186

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Introductionis a set of probability distributions to which we believe the true distribution belongs. It is a subset of all the possible probability distributions. In particular, a parametric model usually forms a finite-dimensional manifold imbedded in the set of all the possible probability distributions. In p

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α-Divergence and α-Projection in Statistical Manifoldgether with a Riemannian metric play a fundamental role in the present theory. Such a structure has not so far been noticed in literature of differential geometry. The dualistic structure of the geometry is elucidated by using the α-flat manifold will turn out to be an interesting generalization of

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