Authors

Bo ZhaoFollow

Date of Completion

5-20-2015

Embargo Period

11-14-2015

Keywords

Generalized Likelihood Ratio Test, Minimum P-Value Statistic, Moving Sums of Squares, Multiple Window Scan Statistic, Variable Window Scan Statistic, Bootstrap

Major Advisor

Professor Joseph Glaz

Associate Advisor

Professor Nitis Mukhopadhyay

Associate Advisor

Professor Vladimir Pozdnyakov

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

In this dissertation scan statistics for detecting a local change in variance are proposed for both one and two dimensional normal observations. When the size of the window where a local change has occurred is known, fixed window scan statistics are proposed. Approximations for the distributions of fixed window scan statistics are investigated. When the correct window size is unknown, variable window scan statistics based on generalized likelihood ratio tests and multiple window minimum P-value scan statistics are developed. When population variance, where the null hypotheses of no change in variance, is also unknown, a conditional approach is employed, for the proposed method of implementing the scan statistics. Conditional variable and multiple window scan statistics are also derived in case both the variance and the window size are unknown. For moderate or large shift in variance, multiple and variable window scan statistics performed well.

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