Doctoral Dissertation

February 27 (Wed) 2-3 pm

Alavi Commons Room, 3302 Rood Hall

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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.