Document Type

Thesis

Degree

Master of Science (MS)

Department

Statistics

First Advisor's Name

B.M.Golam Kibria

First Advisor's Committee Title

Committee Co-Chair

Second Advisor's Name

Florence George

Second Advisor's Committee Title

Committee Co-Chair

Third Advisor's Name

Wensong Wu

Third Advisor's Committee Title

Committee Member

Keywords

Linear regression, Ridge regression, LASSO, Liu, Estimator, Liu type estimator, Simulation

Date of Defense

3-24-2015

Abstract

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Identifier

FI15032146

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