Document Type



Master of Science (MS)



First Advisor's Name

Jie Mi

First Advisor's Committee Title

Co-Committee Chair

Second Advisor's Name

Kai Huang

Second Advisor's Committee Title

Co-Committee Chair

Third Advisor's Name

Florence George


Trivariate Normal Distribution, Permutation-Symmetric Covariance, Missing Data, MLE

Date of Defense



Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.



Thesis_Xing Wang(3551244).tex (117 kB)
Thesis_Xing Wang(tex)



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