Lineer modellerde kestirimler

Regression models are widely used in prediction to predict new future values which provides information about the potential future events and their consequences. Although the ordinary least squares estimator is the best linear unbiased estimator of regression parameters in a linear regression model, we can improve upon the variability of an estimator or a predictor of a regression coefficient when the unbiasedness criterion can be skipped. Also, the predictive performance of a regression model can be adversely affected by both multicollinearity and correlated errors. In spite of biased estimation procedures have been proposed as an alternative to least squares, there has been little analysis of the predictive performance of the resulting equations. This study finds the optimal estimators and predictors of the extended balanced loss function comparing them according to some criteria, and discusses the predictive performance of various biased estimators under only multicollinearity and under multicollinearity and correlated errors simultaneously in terms of the prediction mean squared error. A simulation and numerical examples are conducted to compare the resulting equations.