Iterated WLS Using Residuals for Improved Efficiency in the Linear Model with Completely Unknown Heteroskedasticity

摘要

Iterated weighted least squares (IWLS) is investigated for estimating the regression coefficients in a linear model with symmetrically distributed errors. The variances of the errors are not specified; it is not assumed that they are unknown functions of the explanatory variables nor that they are given in some parametric way. IWLS is carried out in a random number of steps, of which the first one is OLS. In each step the error variance at time t is estimated with a weighted sum of m squared residuals in the neighborhood of t, and the coefficients are estimated using WLS. Furthermore an estimate of the covariance matrix is obtained. If this estimate is minimal in some way the iteration process is stopped. Large sample properties of IWLS are derived. Some particular cases show that the asymptotic efficiency can be increased by allowing more than two steps. Even asymptotic efficiency with respect to WLS with the true error variances can be obtained.