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Paul Shen Master's Thesis 12.12.18.pdf (608 KB)

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Empirical Likelihood Tests For Constant Variance In The Two-Sample Problem

Shen, Paul
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1544187568883762

Abstract Details

2019, Master of Science (MS), Bowling Green State University, Applied Statistics (ASOR).
In this thesis, we investigate the problem of testing constant variance. It is an important problem in the field of statistical influence where many methods require the assumption of constant variance. The question of constant variance has to be settled in order to perform a significance test through a Student t-Test or an F-test. Two of most popular tests of constant variance in applications are the classic F-test and the Modified Levene’s Test. The former is a ratio of two sample variances. Its performance is found to be very sensitive with the normality assumption. The latter Modified Levene’s Test can be viewed as a result of the estimation method through the absolute deviation from the median. Its performance is also dependent upon the distribution shapes to some extent, though not as much as the F-test. We propose an innovative test constructed by the empirical likelihood method through the moment estimation equations appearing in the Modified Levene’s Test. The new empirical likelihood ratio test is a nonparametric test and retains the principle of maximum likelihood. As a result, it can be an appropriate alternative to the two traditional tests in applications when underlying populations are skewed. To be specific, the empirical likelihood ratio test of constant variance uses the optimal weights in summing the absolute deviations of observations from the median values, while the Modified Levene’s test uses the simple averages. It is thus desired that the empirical likelihood ratio test is more powerful than the Modified Levene’s test. Meanwhile, the empirical likelihood ratio test is expected to be as robust as the Modified Levene’s test, as the empirical likelihood ratio test is also constructed via the same distance as the Modified Levene’s test. A real-life data set is used to illustrate implementation of the empirical likelihood ratio test with comparisons to the classic F-test and the Modified Levene’s Test. It is confirmed that the empirical likelihood ratio test performs the best.
Hanfeng Chen, Ph.D. (Advisor)
Wei Ning, Ph.D. (Committee Member)
Christopher Rump, Ph.D. (Committee Member)
28 p.
Mathematics; Statistics
Empirical Likelihood; Statistics; Empirical Likelihood Ratio Test; Constant Variance; T test; F test, Modified Levene Test; Maximum Likelihood

Recommended Citations

Citations

  • Shen, P. (2019). Empirical Likelihood Tests For Constant Variance In The Two-Sample Problem [Master's thesis, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1544187568883762

    APA Style (7th edition)

  • Shen, Paul. Empirical Likelihood Tests For Constant Variance In The Two-Sample Problem. 2019. Bowling Green State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1544187568883762.

    MLA Style (8th edition)

  • Shen, Paul. "Empirical Likelihood Tests For Constant Variance In The Two-Sample Problem." Master's thesis, Bowling Green State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1544187568883762

    Chicago Manual of Style (17th edition)

bgsu1544187568883762
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This open access ETD is published by Bowling Green State University and OhioLINK.