generalized regression estimators

Sampling weights are calibrated according to the theory of calibration when the sum of population total for auxiliary variables is known. Under known population، totals for auxiliary variables and some conditions Devile and Sarndal showed that generalized regression estimators could approximate calibration estimators and their variances. In this paper، under unknown population totals for auxiliary variables، an estimator for the population total is proposed and its variance is obtained. It is shown that our estimator for the population total is more efficient than the Horvitz-Thompson estimators by theoretically and simulation results.

In many statistical systems, a type of survey called “sampling over time” is common, which repeats continuously over time. One method of sampling over time is panel survey. Panel survey is a method in which a “fixed sample” is contacted during different waves. The most important challenge in a panel survey is debility in providing response from some sample units and having non-response that usually causes bias or in some cases leads to increasing variance of estimates. In addition to item nonresponse, in panel surveys, also there is another type of nonresponse called “wave nonresponse”. Wave nonresponse occurs when one or more waves of panel data are missing for a unit that has provided data for at least one wave. A particular aspect of wave nonresponse is attrition in which sampling unit is excluded from the survey. Weighting is a method of reducing undesirable effects of a wave nonresponse. Calibration estimator is one of the weighting methods. In this article after introducing primary concepts of panel survey, types of missingness in panel surveys and missing mechanisms, calibration estimators is introduced as a method of weighting missing data. Then by using of British Household Panel Survey data, calibration estimator method is compared with generalized regression estimator with respect to different criteria such as absolute relative bias, mean square error and estimated asymptotic relative efficiency. The findings of the study show that when correlation between two waves is high and missing mechanism is at random, calibration estimator method has better performance than some other methods.