IMPROVING SURVEY-WEIGHTED LEAST-SQUARES REGRESSION

The weighted least squares (WLS) estimator is often employed in linear regression using complex survey data to deal with the bias in ordinar y least squares (OLS) arising from informative sampling. In this paper a 'quasi-Aitken WLS' (QWLS) estimator is proposed. QWLS modifies WLS in the same way that Cragg's quasi-Aitken estimator modifies OLS. It w eights by the usual inverse sample inclusion probability weights multi plied by a parameterized function of covariates, where the parameters are chosen to minimize a variance criterion. The resulting estimator i s consistent for the superpopulation regression coefficient under fair ly mild conditions and has a smaller asymptotic variance than WLS.