The Annals of Statistics

Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach

Ichi Okamoto, Shun-Ichi Amari, and Kei Takeuchi

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Abstract

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.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 961-981.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348131

Digital Object Identifier
doi:10.1214/aos/1176348131

Mathematical Reviews number (MathSciNet)
MR1105855

Zentralblatt MATH identifier
0737.62067

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62F12: Asymptotic properties of estimators

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

Citation

Okamoto, Ichi; Amari, Shun-Ichi; Takeuchi, Kei. Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach. Ann. Statist. 19 (1991), no. 2, 961--981. doi:10.1214/aos/1176348131. https://projecteuclid.org/euclid.aos/1176348131


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