A New Modified Generalized Two Parameter Estimator for linear regression model

Abstract

The Ordinary Least Squares estimator estimates the parameter vectors in a linear regression model. However, it gives misleading results when the input variables are highly correlated, emanating the issue of multicollinearity. In light of multicollinearity, we wish to obtain more accurate estimators of the regression coefficients than the least square estimators. The main problem of least square estimation is to tackle multicollinearity so as to get more accurate estimates. In this paper, we introduce a New Modified Generalized Two Parameter Estimator by merging the Generalized Two Parameter Estimator and the Modified Two Parameter Estimator and compare it with other known estimators like Ordinary Least Squares Estimator, Ridge Regression Estimator, Liu estimator, Modified Ridge Estimator, Modified Liu Estimator and Modified Two Parameter Estimator. Mean Squared Error Matrix criterion was used to compare the new estimator over existing estimators. The estimation of the biased parameters is discussed. Necessary and sufficient conditions are derived to compare the proposed estimator with the existing estimators. The excellence of the new estimator over existing estimators is illustrated with the help of real data set and a Monte Carlo simulation study. The results indicate that the newly developed estimator is more efficient as it has lower mean square error.