SOME ADJUSTED RIDGE ESTIMATORS AND ITS CORRELATION-FREE VERSION

The recently developed Adjusted Ridge Estimator (ARE) for handling multicollinearity problem in Linear Regression model does not require the use of the biasing or ridge parameter, K, unlike the Ridge Regression Estimators (RRE) rather it requires a diagonalization of the correlation vector of the explanatory variables and the dependent variable being raised to a power of half In this research, the effects of other powers on the Adjusted Ridge Regression Estimator were investigated and a correlation-free Adjusted Ridge Regression Estimator (CFARE) was developed. In order to examine the performances of some existing ridge estimators; the Ordinary Ridge Estimator (ORE) and Generalized Ridge Estimator (GRE), various AREs and the CF ARE; Monte Carlo experiments were performed one thousand (1000) times on two (2) linear regression models with three (3) and seven (7) explanatory variables exhibiting five (5) degrees of multicollinearity, classified as high ( p=.8 and 0.9) and severe (p=0.99, 0.999 and 0.9999), and four (4) levels of error variance, classified as small (0'2=0.25 and 1) and large (a2=25 andl OO) at eight (8) sample sizes (n=l 0,20,30,40,50, 1 00,250 and 500). The Mean Square Error (MSE) criterion was used to examine the estimators and the number of times each estimator had the minimum MSE was counted at each combination of classifications. The results revealed that with large variances: the most frequent efficient estimator is generally CF ARE except at high multicollinearity when p=3 and p=7 and the sample sizes are n ;::::so and n>= 40 respectively. At these instances, the most frequent efficient estimator is GRE. Furthermore with small variances, the most frequent estimator is either ORE or GRE or AREs with its power between 0.1 and 0.7 or CF ARE. In conclusion, the research recommends the use of CF ARE when the error standard deviation is large and either ORE or AREs with powers between 0.25 and 0.7 when the error standard deviation is small, for the parameter estimation of Linear Regression model with multicollinearity problem.