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Shu, Wun-Yi 2014-12-16T06:18:20Z 2014-12-16T06:18:20Z 10000-01-01 1987 1987 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. Made available in DSpace on 2014-12-16T06:18:20Z (GMT). No. of bitstreams: 1 8721760.pdf: 2383663 bytes, checksum: 1f554e8526432b484b8c0dd2ad7a427f (MD5) Previous issue date: 1987 Embargo set by: Seth Robbins for item 71425 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 92 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987. http://hdl.handle.net/2142/71259 (UMI)AAI8721760 Statistics Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.