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Unconventional Approach with the Likelihood of Correlation Matrices

Song, Myung Soon (2011) Unconventional Approach with the Likelihood of Correlation Matrices. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Numerical approximations are important research areas for dealing with complicated functional forms. Techniques for developing accurate and efficient calculation of combined likelihood functions in meta-analysis are studied. The first part of the thesis introduces a B-spline approximation for making a parsimonious model in the simplest case(2-dimensional case) of correlation structure. Inference about the correlation between vitamin C intake & vitamin C serum level is developed by using likelihood intervals and the MLE, along with comparison with conventional methods. The second part studies a multivariate numerical integration method for developing a better approximation of the likelihood for correlation matrices. Analyses for (1) intercorrelations among Math, Spatial and Verbal scores in an SAT exam and (2) intercorrelations among Cognitive Anxiety, Somatic Anxiety and Self Confidence from Competitive State Anxiety Inventory (CSAI-2) are explored. Algorithms to evaluate likelihood and to find the MLE is developed. Comparison with two conventional methods (joint asymptotic weighted average method & marginal asymptotic weighted average method) is shown.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Song, Myung
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairGleser, Leon J. gleser@pitt.eduGLESER
Committee MemberGreenhouse,
Committee MemberIyengar, Satishssi@pitt.eduSSI
Committee MemberCheng, Yuyucheng@pitt.eduYUCHENG
Date: 30 September 2011
Date Type: Completion
Defense Date: 19 May 2011
Approval Date: 30 September 2011
Submission Date: 31 May 2011
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: correlation matrix; likelihood; meta-analysis; numerical integration
Other ID:, etd-05312011-162131
Date Deposited: 10 Nov 2011 19:46
Last Modified: 15 Nov 2016 13:44


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