Abstract

In sample survey, it is expected that the information would be collected from all the selected units in the sample, but practically, it is generally not possible because of non-response. Some of the units may not respond or may not be contacted during the survey period. This work focuses on domain estimation of population mean with sub-sampling the nonrespondents. In this study, we consider calibration technique as a method of correcting non-response in domains of study by minimizing the chi-square distance function between the weight of the main estimator and the calibrated weight subject to the formulated constraint on the auxiliary variable. As a result, two estimators are proposed; these are the ratio estimator for domain mean and a ratio estimator for double sampling. Bias and Mean Square Error (MSE) for the proposed estimators are derived. We have used an auxiliary variable to estimate the population mean assuming that the nonresponse is observed only on the study variable. The proposed estimators and the existing estimators where compared empirically in the domains with small sampling units and two populations where considered in terms of the MSE and Percentage Relative Efficiency (PRE). We considered two cases where non-responses are uniform in the two strata at approximately (30%) and a case where the non-response rates are different with 20% and 40% in strata 1 and 2 respectively. The proposed estimators are more efficient than the existing estimators. 

Keywords

auxiliary variable, calibration, non-response, ratio estimator, sub-sampling, domain