Colloquium

Colloquium


Doctoral Dissertation
February 27 (Wed) 2-3 pm
Alavi Commons Room, 3302 Rood Hall

A Computational Method for Estimating and Finding the Confidence Interval of the Ratio of the Scale Parameters in the Two-Sample Problem

Mona Abdullah Alduailij
Department of Statistics
Western Michigan University

Testing equality of variances between two samples is applied in various fields. In the absence of normal assumptions, the usual equality of variance tests do not yield robust results. There are many parametric and nonparametric methods for estimating the scale parameter; yet a distribution-free method for estimating and finding the confidence 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 calculating an estimator and confidence interval of the ratio of scale parameters for the two-sample problem. A comparison between existing parametric and nonparametric rank tests will be conducted. These 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.

Porpoerties of the developed algorithm 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 our proposed estimate will be compared with the available parametric methods 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. The proposed algorithm supports the assertion that the estimator and 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, real data from cloud-based computing environment will be analyzed.

All statistics students are encouraged to attend.

 

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