Generalized Calibration Estimator of Population Mean for Stratified Sampling in the Presence of Non-response

Abstract

The present research focuses on developing a comprehensive mathematical framework for estimating the population mean by applying the calibration approach when some units don’t respond (non-response). This study focuses mainly on stratified sampling. The generalized form of the calibration estimators was obtained by minimizing a chi-square type distance function while simultaneously meeting a set of m conditions. The purpose of formulating this general form is to facilitate the deduction of the mean squared error of several previously proposed calibration estimators of the mean for well-stratified groups involving non-response. The general form of the calibration estimators not only allows for obtaining previously proposed calibration-based estimators but also opens the door for developing numerous improved calibration estimators for population mean in the non-response scenarios. The calibration estimator proposed by Dykes et al. (Commun Stat-Theory Methods 44:3403-3427, 2015) and four new calibration estimators were also derived using the suggested general form to support our mathematical framework. The purpose of formulating this general form is to facilitate the deduction of the mean squared error of several previously proposed calibration estimators of the mean for well-stratified groups involving non-response. The simulation study has also been performed in R software generating five different data sets. It exhibited that the proposed calibration estimators perform better than the existing estimators given by Hansen and Hurwitz (1946) as well as Dykes et al. (Commun Stat-Theory Methods 44:3403-3427, 2015) in the presence of non-response. © The Indian Society for Probability and Statistics (ISPS) 2025.