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Testing on the Common Mean of Normal Distributions Using Bayesian Method

Li, Xiaosong
http://rave.ohiolink.edu/etdc/view?acc_num=case1301420382

Abstract Details

2011, Doctor of Philosophy, Case Western Reserve University, Statistics.
Of all the problems in the statistical sciences, one of the oldest is the inference on a common mean of several different normal populations with unknown and probably unequal variance. There are several ways to make the inference on the common mean. The most common way is point estimation, which uses sample data to calculate a single value serving as a best guess for the unknown population mean; the second way is interval estimation, which constructs an interval of possible values of the unknown mean; and the third one is to conduct a hypothesis test which assumes all populations have the same mean as the null hypothesis. The first two types of inference are widely studied in the literature in the past, but little attention has been paid to the third type. One of the reasons may be that the test statistic(s) of the hypothesis test usually involves a complicated sampling distribution(s) which requires lots of computational resources out of reach of the ordinary researcher. With the fast development of new technology which is widely accessible on a personal computer, this is no longer an obstacle and more research has been done in this area. In their 2008 paper, Dr. Ching-Hui Chang and Dr. Nabendu Pal described several methods that can be used to test hypotheses concerning the common mean of several normal distributions with unknown variances. The methods they proposed are the likelihood ratio test (LRT), two tests based on the Graybill-Deal Estimator (GDE) and the test based on the maximum likelihood estimator (MLE). In this thesis, several procedures based on the Bayesian method are proposed, simulation studies of power and robustness of the newly proposed tests, the LRT and GDE test are performed and discussed. The new tests proposed in this thesis are either based on the assumption that the posterior distribution of the common mean µ following some specific distribution (t or normal), or is free of assumption of distribution, and is based on slice sampling (Neal, 2003), Highest Posterior Density (HPD) Method (Berger 1985) or a modified version of HPD.
Patricia Williamson (Advisor)
Joseph Sedransk (Committee Member)
Wojbor Woyczynski (Committee Member)
Stephen Ganocy (Committee Member)
128 p.
Statistics
Meta-Analysis; Bayesian method

Recommended Citations

Citations

  • Li, X. (2011). Testing on the Common Mean of Normal Distributions Using Bayesian Method [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1301420382

    APA Style (7th edition)

  • Li, Xiaosong. Testing on the Common Mean of Normal Distributions Using Bayesian Method. 2011. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1301420382.

    MLA Style (8th edition)

  • Li, Xiaosong. "Testing on the Common Mean of Normal Distributions Using Bayesian Method." Doctoral dissertation, Case Western Reserve University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=case1301420382

    Chicago Manual of Style (17th edition)

case1301420382
852
© 2011, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.