Advances and Applications in Statistics
Volume 50, Issue 4, Pages 293 - 314
(April 2017) http://dx.doi.org/10.17654/AS050040293 |
|
A MATHEMATICAL PROGRAMMING APPROACH FOR LIU-TYPE ESTIMATOR
Rasha Ebaid, Rasha Farghali and Samah Abo-El-Hadid
|
Abstract: Multicollinearity is a well known problem in the linear regression model. It refers to the phenomenon where the explanatory variables are highly correlated and accordingly, least squares (LS) estimators have large mean squared error (MSE) and large condition index (CI). Hoerl and Kennard [12] proposed a single-parameter ridge regression as a means for combating multicollinearity. Although ridge regression is superior to LS regression, it did not achieve the two desired goals: minimum MSE and CI. Liu [23] proposed a two-parameter estimator where the first parameter is chosen so as to minimize the CI to a desired level and then the second parameter is chosen to minimize the MSE. Several estimators have been introduced in the literature for selecting the two parameters separately. In this paper, we propose a new estimator where the two parameters are selected simultaneously to minimize CI and MSE using a mathematical programming approach. A simulation study is conducted to compare the performance of our estimator with some of the well known estimators in the literature. Finally, we illustrate our findings on a real data application. |
Keywords and phrases: multiple regression, Liu-type estimators, multicollinearity mathematical programming, condition index, MSE. |
|
Number of Downloads: 435 | Number of Views: 1376 |
|