Calibrated Estimators of Population Mean for a Mail Survey Design

Abstract

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.

Keywords::

• Mail survey designs
• Calibrated estimators
• Estimation of mean
• Relative efficiency
• Auxiliary information.

Mathematical Subject Classification:

• 62D05.

Acknowledgments

The authors are thankful to the Editor-in-Chief Professor Dr. N.. Balakrishnan and, two referees for these fruitful comments on the original version of this article. The authors are also thankful to R Development Core Team (2009), R: A Language and Environment for Statistical Computing, (http://www.R-project.org), for using R coding in the simulation study and analyzing datasets. This work is a part of Lee Dykes’ undergraduate project at TAMUK. The detailed derivations of the results can be had from the authors on a request. At present Lee Dykes is working as Senior Applications Developer, Global Impact, 1616 Cheyenne St., Portland, TX 78374.