Calibrated Estimators of Population Mean for a Mail Survey Design

In this article, we consider the problem of estimating the population mean of a study variable in the presence of non-response in a mail survey design. We introduce calibrated estimators of the population mean of a study variable in the presence of a known auxiliary variable. Using simulation the proposed calibrated estimators of population mean are compared to the Hansen and Hurwitz (1946) estimator under different situations for fixed cost as well for fixed sample size. The results are then extended for the use of multi-auxiliary information and stratified random sampling. We consider the problem of estimating the average total family income in the US in the presence of known auxiliary information on total income per person, age of the person, and poverty. We compute the relative efficiency of the proposed estimator over the Hansen and Hurwitz (1946) estimator through the use of large real datasets. Results are also presented for sub-populations consisting of whites, blacks, others, and two or more races in addition to considering them together in a population.