Limit Theorems for Processes and Stopping Rules in Adaptive Sequential Estimation

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}(\α\sb{n}})-σ\sp2(α\*)) are derived. These results are of independent interest.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Shu, Wun-Yi

• Statistics

Identifier

(UMI)AAI8721760

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71259