Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

B. M. Golam Kibria

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Florence George

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Wensong Wu

Third Advisor's Committee Title

Committee Member

Keywords

Statistics, Ridge Regression, Poisson Regression, Monte Carlo Simulation, Poisson, Multicollinearity, Correlation, Poisson Ridge Regression

Date of Defense

3-28-2018

Abstract

Multiple regression models play an important role in analyzing and making predictions about data. Prediction accuracy becomes lower when two or more explanatory variables in the model are highly correlated. One solution is to use ridge regression. The purpose of this thesis is to study the performance of available ridge regression estimators for Poisson regression models in the presence of moderately to highly correlated variables. As performance criteria, we use mean square error (MSE), mean absolute percentage error (MAPE), and percentage of times the maximum likelihood (ML) estimator produces a higher MSE than the ridge regression estimator. A Monte Carlo simulation study was conducted to compare performance of the estimators under three experimental conditions: correlation, sample size, and intercept. It is evident from simulation results that all ridge estimators performed better than the ML estimator. We proposed new estimators based on the results, which performed very well compared to the original estimators. Finally, the estimators are illustrated using data on recreational habits.

Identifier

FIDC006538

Available for download on Sunday, October 21, 2018

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