New generalized regression estimator in the presence of non response under unequal probability sampling

Abstract

In this paper, we propose a new generalized regression estimator for the problem of estimating the population total using unequal probability sampling without replacement. A modified automated linearization approach is applied in order to transform the proposed estimator to estimate variance of population total. The variance and estimated value of the variance of the proposed estimator is investigated under a reverse framework assuming that the sampling fraction is negligible and there are equal response probabilities for all units. We prove that the proposed estimator is an asymptotically unbiased estimator and that it does not require a known or estimated response probability to function.

Keywords:

• Automated linearization approach
• generalized regression estimator
• response probability
• reverse framework

Acknowledgments

We are grateful to Dr. Yves Berger (University of Southampton, UK) for suggesting this topic and to the referees for helpful comments. We are also grateful to Dr. Elvin J. Moore for proofreading the manuscript.