A comparison of two methods for estimating optimal weights in regression analysis

Abstract

Two methods for estimating the variance function Var{Y\X = X) in weighted regression analysis are studied via simulation.The first method assumes that Var(Y|X= x) is a known power of the regression function E(Y|X= x), and estimates the coefficient vector ßusing iteratively reweighted least squares. In the second method, Var(Y|X= x) is estimated directly using a nonparametric regression technique.The results show that the first method can perform very poorly in the presence of strong heteroscedasticity, and that the second method may provide an effective alternative in such cases.

Keywords:

• Gauss-Markov weights
• ordinary least squares
• iteratively reweighted least squares
• kernel estimators of regression functions