A Study on the Correlation of Bivariate And Trivariate Normal Models

Authors

Maria del Pilar Orjuela, Florida International UniversityFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

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

Keywords

Bivariate Normal Distribution, Trivariate Normal Distribution, Equal Variances and equal Covariances, Correlation Coefficient

Date of Defense

11-1-2013

Abstract

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population.

This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

Identifier

FI13120413

Recommended Citation

Orjuela, Maria del Pilar, "A Study on the Correlation of Bivariate And Trivariate Normal Models" (2013). FIU Electronic Theses and Dissertations. 976.
https://digitalcommons.fiu.edu/etd/976