Generalized Least Squares and Weighted Least Squares Estimation Methods for Distributional Parameters

Abstract

Regression procedures are often used for estimating distributional parameters because of their computational simplicity and useful graphical presentation. However, the resulting regression model may have heteroscedasticity and/or correction problems and thus, weighted least squares estimation or alternative estimation methods should be used. In this study, we consider generalized least squares and weighted least squares estimation methods, based on an easily calculated approximation of the covariance matrix, for distributional parameters. The considered estimation methods are then applied to the estimation of parameters of different distributions, such as Weibull, log-logistic and Pareto. The results of the Monte Carlo simulation show that the generalized least squares method for the shape parameter of the considered distributions provides for most cases better performance than the maximum likelihood, least-squares and some alternative estimation methods. Certain real life examples are provided to further demonstrate the performance of the considered generalized least squares estimation method.