Estimation and testing of parameters under constraints for correlated data Public Deposited

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Last Modified
  • March 20, 2019
Creator
  • Farnan, Laura
    • Affiliation: Gillings School of Global Public Health, Department of Biostatistics
Abstract
  • This dissertation work is motivated by problems encountered in the analysis of some toxicological and clinical trials data, where repeated measurements are made on each subject, and the investigator expects trends in mean response among dose groups and/or time points. There are two components to this research. The first component focuses on estimation of parameters subject to inequality constraints, when the covariance matrix of the unrestricted estimator is non-diagonal. In particular, statistical properties of several available constrained estimators are investigated theoretically and via simulations under different covariance structures. The second component is developing a simple, yet statistically appropriate methodology for testing hypotheses in a linear mixed effects model with an inequality constraint in the alternative. Since in many applications one cannot be certain about the normality of the data, a bootstrap based methodology using MINQUE-Williams' type test is implemented for testing the above hypotheses. The resulting methodology is illustrated by re-analyzing the blood mercury level data provided in Cao et al. (2011).
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  • In Copyright
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  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biostatistics, Gillings School of Global Public Health."
Advisor
  • Peddada, Shyamal Das
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Place of publication
  • Chapel Hill, NC
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  • Open access
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