Combined Estimators as alternative to Ordinary Least Square Estimator

Abstract

The Ordinary Least Square (OLS) estimator of the classical linear regression model is Best Linear Unbiased Estimator (BLUE) provided the assumptions of the model are not violated. In this paper, attempt is made to combine some Feasible Generalized Least Square (FGLS) estimators with the estimator based on Principal Component (PC) Analysis and compare their finite sampling properties and goodness-of-fit statistics with that of the OLS estimator through Monte Carlo Simulation study. Using both normally and uniformly distributed variables as regressors, results show that the estimators perform better and similar with increased sample sizes and that the results from normally distributed variables are much better on the basis of the criteria. The OLS estimator remains the most efficient and the combined estimators compete favorably with the estimator (OLS) especially when the sample size is large. The combined estimators are frequently more efficient than their separate counterpart estimator, asymptotically equivalent and best in terms of their goodness-of-statistics estimates. Thus, the combined estimators have the advantage of being used better for prediction.