Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation
Shu, Wun-Yi
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https://hdl.handle.net/2142/71259
Description
Title
Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation
Author(s)
Shu, Wun-Yi
Issue Date
1987
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Abstract
This thesis deals with the asymptotic behavior of stopping rules ${\rm T\sb{A}}$ and ${\rm T\sb{d}}$ proposed by Martinsek (Ann. Statist., 12 (1984):533-550). The asymptotic normality of these stopping rules, when A tends to infinity and d tends to zero respectively, is proved. In the course of proving this, results about the limiting distribution of a closely related stochastic process and of ${\rm n\sp{1/2}\lbrack S\sbsp{n}{2}(\\alpha\sb{n}})-\sigma\sp2(\alpha\*)$) are derived. These results are of independent interest.
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