Variance of Weighted Regression Estimators when Sampling Errors are Independent and Heteroscedastic

Abstract

Abstract General results are obtained for an approximation to the variance of a weighted regression estimator in which the weights are sample estimators of unknown unpatterned variances. Independent normally distributed errors are specified for the linear response model used in the development. Applications to four examples of weighted sample means and linear regression in a single factor are studied. The most important practical conclusion drawn from the results of these examples is that each estimated weight should be based on at least ten degree of freedom.