Asymptotically pointwise optimal allocation rules for continuous-time processes in Bayes sequential estimation

In this article, the concept of asymptotic pointwise optimality in a single continuous-time process provided by Hwang (2001) is extended to more than one continuous-time process. We propose an asymptotically pointwise optimal (APO) rule, which consists of a sequential allocation procedure and a stop...

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Bibliographic Details
Published inSequential analysis Vol. 43; no. 4; pp. 497 - 512
Main Author Hwang, Leng-Cheng
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.10.2024
Taylor & Francis Ltd
Subjects
Asymptotic methods
Asymptotic properties
Asymptotically nondeficient
asymptotically optimal
asymptotically pointwise optimal
Bayes sequential estimation
Bayesian analysis
Optimization
Primary 62L12
Secondary 62C10
sequential allocation
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ISSN0747-4946
1532-4176
DOI10.1080/07474946.2024.2425301

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Summary:In this article, the concept of asymptotic pointwise optimality in a single continuous-time process provided by Hwang (2001) is extended to more than one continuous-time process. We propose an asymptotically pointwise optimal (APO) rule, which consists of a sequential allocation procedure and a stopping time, and derive some properties of asymptotic optimality of the rule. In particular, some APO rules are proposed in the Bayes sequential estimation problem for several Poisson processes under both squared error loss and linear exponential loss functions. They are shown to be asymptotically optimal for arbitrary priors and asymptotically nondeficient for conjugate priors.
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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2024.2425301