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Doctoral Dissertation Announcement
Candidate: Mona Abdullah Alduailij
Doctor of Philosophy
Title: A Computational Method for Estimating and Finding the Confidence Interval of the Ratio of the Scale Parameters in the Two-Sample Problem
Dr. Gerald L. Sievers, Chair
Dr. Jung Chao Wang
Dr. Jeff Terpstra
Dr. Ala Al-Fuqaha
Date: Wednesday, February 27, 2013 2 p.m. to 4 p.m.
3302 Rood Hall
Testing equality of variances between two samples is applied in various fields. However, in the absence of non-normal assumptions, equality of variance tests do not yield robust results. In real life situations, the absence of such assumptions is even evident, which calls for more reliable tests to accommodate for the lack of these assumptions. There are abundant parametric and nonparametric methods for estimating the scale parameter; yet a distribution-free method for estimating and finding the confident interval of the ratio of scale parameters in the two-sample problem would be a reliable alternative.
This dissertation proposes a computational iterative method for finding the estimator and confidence interval of the ratio of the scale parameters for the two-sample problem. A comparison between the existing parametric and nonparametric rank tests for the two-sample scale problem which include linear rank tests and folded rank tests with different score functions, Lehmann test, jackknife test, Sukhatme test, placement tests, permutation tests and the classical Levene tests will be conducted.
The developed algorithm of estimation and finding the confidence interval of the scale parameters will be examined. A Monte Carlo simulation will be used to study the performance of our algorithm under symmetric and asymmetric distributions for different sample sizes. The efficiency of the estimated parameters will be compared with the available parametric method for estimation. Also, the efficiency of the proposed confidence interval will be analyzed by computing the length of the interval and its probability of coverage. In general, our algorithm performs better than the available methods for estimating the ratio of scale parameters in the two-sample problem.
This work suggests the robustness of the Lehmann test and the Folded Klotz test for testing the equality of variances. This suggestion is supported by the proposed algorithm, which asserts that the estimator and the confidence interval of Lehmann test and the Folded Klotz test are superior compared to other tests in estimating the ratio of scale parameters in the two-sample problem. Finally, a real data from cloud-based computing environment will be analyzed.