ASYMPTOTIC THEORY OF SEQUENTIAL ESTIMATION - DIFFERENTIAL GEOMETRICAL APPROACH

• 成果类型: Article
• 署名作者: OKAMOTO, I; AMARI, S; TAKEUCHI, K
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348131
• 发表日期: 1991
• 页码: 961-981
• 关键词: fisher information; EFFICIENCY

摘要

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.