Date of Completion

7-21-2016

Embargo Period

7-20-2019

Keywords

robust scan statistics; moving median; rejection accuracy; minimum p-value statistics; multiple window scanning; distribution free

Major Advisor

Joseph Glaz

Associate Advisor

Nitis Mukhopadhyay

Associate Advisor

Vladimir Pozdnyakov

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Campus Access

Abstract

The major part of this dissertation is focusing on robust scan statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers. I investigate the performance of scan statistics based on moving medians of the observed data. When no outliers are present, approximations and inequalities are derived for tail probabilities of fixed window scan statistics based on moving medians. The performance of these scan statistics are evaluated and compared to the performance of scan statistics, based on moving sums, that have been previously investigated in the statistical literature. Numerical results based on a simulation study, for independent and identically distributed (iid) normal observations with known variance, indicate that in presence of outliers, the scan statistics based on moving medians outperform the scan statistics based on moving sums. These results are extended for iid normal observations when the population variance is unknown. Moreover, the performance of multiple window scan statistic based on moving medians for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the size of the window where a change has occurred is unknown, has also been evaluated. Scan statistic for detecting a local change in the population mean of iid observations from a continuous unknown distribution, in presence of outliers is investigated as well. Both fixed window robust scan statistics and multiple window robust scan statistics performed well in each case for moderate or large shift in population mean.

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