Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach

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...

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Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 19(1991), 2, Seite 961-981
1. Verfasser: Okamoto, Ichi (VerfasserIn)
Weitere Verfasser: Amari, Shun-Ichi, Takeuchi, Kei
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1991
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Asymptotic theory conformal transformation covariance stabilization differential geometry higher-order asymptotics sequential estimation statistical curvature stopping rule Mathematics Behavioral sciences
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520 |a 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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