New Population Total Estimators under Stratified Sampling Design in the Presence of Nonresponse

Abstract

In this paper we propose new estimators for population total in the presence of nonresponse with both a known and unknown response probability. The proposed estimators are investigated under stratified sampling with two assumptions within each stratum: uniform nonresponse and an overall negligible sampling fraction. We show in theory that one of our proposed estimators with a known response probability is unbiased, while the other estimators are asymptotically unbiased, and the variance estimation of the proposed estimators are all asymptotically unbiased. Finally, we compared the efficiency of the proposed estimators through a numerical comparison. The results showed that the proposed estimators performed well with a very small relative bias, especially for the proposed estimator with an unknown response probability which had a smaller relative root mean square error when compared to the others.