SOURCE:

Faculty: Physical Sciences
Department: Statistics

CONTRIBUTORS:

Uzuke, C. A
Mbegbu, J.I

ABSTRACT:

Ridge Regression is one of the techniques of solving the problem of multicollinearity. The idea in ridge regression is to add a small positive number (k > 0) to the diagonal elements of the matrix in order to obtain a ridge regression estimate that shortens the length of the regressor vector. The problems in the use of the eigenvalues of the correlation matrix to obtain the ridge estimator were considered and new methods of estimating the ridge parameter k were proposed. Mean Square Error (MSE) and Prediction Sum of Square (PRESS) criteria were used to compare the performances of the proposed estimators with some existing estimators via Monte Carlo Simulation. A multicollinear data on Nigerian Economic Variables was also used to investigate the performance of the proposed ridge estimators. The proposed ridge estimator when the eigenvalues of the correlation matrix are skewed exhibited smaller MSE and PRESS than other existing ridge estimators. Furthermore, the proposed ridge estimators when there is an outlier among the eigenvalues of the correlation matrix exhibited smaller values of MSE and PRESS than other existing estimators considered. The result obtained from simulation study showed that as the correlation coefficient increases, the MSE of the ridge estimators decreases as the number of explanatory variables increases, the MSE and the PRESS of the ridge estimators decrease respectively.