Calibration technique for compensation of non-response in domains of study with probability proportional to size

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 non-respondents using probability proportional to size. 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. The bias and mean square error (MSE) for the proposed estimators are derived. The use an auxiliary variable to estimate the population mean assuming that the non-response is observed only on the study variable is adopted. The proposed estimator and the existing estimators were compared empirically in the domains with small sampling units and two populations were considered in terms of the MSE and Percentage Relative Efficiency (PRE). Also, two cases were considered, where non-responses are uniform in the two strata at approximately (30%) and a case where the nonresponse rates are different with 20% and 40% in strata 1 and 2 respectively. The proposed estimator gained more efficiency than the existing estimators. However, the proposed estimator performed better in case II than in case I in some domains but the aggregate result suggests otherwise in both populations.