Joint calibration estimator for dual frame surveys

Abstract

Many dual frame estimators have been proposed in the statistics literature. Some of these estimators are theoretically optimal but hard to apply in practice, whereas others are applicable but have larger variances than the first group. In this paper, a Joint Calibration Estimator (JCE) is proposed that is simple to apply in practice and meets many desirable properties for dual frame estimators. The JCE is asymptotically design unbiased conditional on the strong relationship between the estimation variable and the auxiliary variables employed in the calibration. The JCE achieves better performance when the auxiliary variables can fully explain the variability in the study variables or at least when the auxiliary variables are strong correlates of the estimation variables. As opposed to the standard dual frame estimators, the JCE does not require domain membership information. Even if included in the JCE auxiliary variables, the effect of the randomly misclassified domains does not exceed the random measurement error effect. Therefore, the JCE tends to be robust for the misclassified domains if included in the auxiliary variables. Meanwhile, the misclassified domains can significantly affect the unbiasedness of the standard dual frame estimators as proved theoretically and empirically in this paper.