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 Title: Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation Author(s): Shu, Wun-Yi Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(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. Issue Date: 1987 Type: Text Description: 92 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987. URI: http://hdl.handle.net/2142/71259 Other Identifier(s): (UMI)AAI8721760 Date Available in IDEALS: 2014-12-16 Date Deposited: 1987
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