Calibration Estimation of Population Proportion in Probability Proportional to Size Sampling in the Presence of Non-Response

Abstract

Objectives: In this article, we addressed the problem of estimation of the finite population proportion under the Probability Proportional to Size (PPS) sampling technique, when the complete information is unavailable due to the presence of non-response. We developed calibrated estimators of the population proportion under PPS sampling in the presence of nonresponse based on the availability of auxiliary information. Methods: The expressions for the mean squared errors of the suggested estimators were developed to the first order of approximation. The developed estimators of the population proportion are compared with the design-based Horvitz-Thompson estimator and Horvitz-Thompson type calibration estimator which were obtained on the complete response units along with the design-based Hansen and Hurwitz type estimator in the presence of non-response. A Simulation study has also been conducted to support the performance of the developed estimators of population proportion with the help of two real datasets, by computing Percentage Absolute Relative Bias (%ARB) and Percentage Relative Root Mean Squared Error (%RRMSE) using R software. Findings: The simulation study supported the performance of the developed estimators of the finite population proportion based on %ARB and %RRMSE. The proposed calibration estimators of population proportion are more efficient than the other considered estimators in the presence of non-response. Novelty: The proposed new calibrated estimators have practical implications in the estimation of finite population proportions. Keywords: Auxiliary information, Calibration Approach, Non­response, Population proportion, PPS sampling