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June, 1991 Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach
Ichi Okamoto, Shun-Ichi Amari, Kei Takeuchi
Ann. Statist. 19(2): 961-981 (June, 1991). DOI: 10.1214/aos/1176348131


Sequential estimation continues observations until the observed sample satisfies a prescribed criterion. Its properties are superior on the average to those of nonsequential estimation in which the number of observations is fixed a priori. A higher-order asymptotic theory of sequential estimation is given in the framework of geometry of multidimensional curved exponential families. This gives a design principle of the second-order efficient sequential estimation procedure. It is also shown that a sequential estimation can be designed to have a covariance stabilizing effect at the same time.


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Ichi Okamoto. Shun-Ichi Amari. Kei Takeuchi. "Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach." Ann. Statist. 19 (2) 961 - 981, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0737.62067
MathSciNet: MR1105855
Digital Object Identifier: 10.1214/aos/1176348131

Primary: 62F10
Secondary: 62F12

Keywords: Asymptotic theory , conformal transformation , covariance stabilization , Differential geometry , higher-order asymptotics , sequential estimation , statistical curvature , stopping rule

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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