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.

Accumulating Birth Histories Across Surveys for Improved Estimates of Child Mortality

“…Cumulating data across several surveys achieves many goals, such as (1) increasing sample size, which produces reliable estimates with reduced estimated variance on the national level, or on small geographic and non-geographic domains; (2) estimating change across different surveys (Kalton, 2009;Robert & Binder, 2009;Thomas & Wannell, 2009). The cumulating technique has also been used to combine different samples in multiple frame designs to overcome frame non-coverage problems (Elkasabi, 2015;Elkasabi et al, 2015;Lohr, 2011). Furthermore, it has been used to combine rolling samples of the same survey.…”

“…Different methods can be used to choose the values of the composite factor ̂ i , such as to minimize the variance of the cumulated estimate in (2) or to account for the effective sample size for each of the periodic samples (Chu et al, 1999;Korn & Graubard, 2011;Roberts & Binder, 2009). These methods are motivated by estimation methods developed for surveys with multiple frame designs (Elkasabi et al, 2015;Lohr, 2011;Skinner & Rao, 1996). We chose to use one of the common multiple frame estimators: the multiplicity estimator.…”