Calibration Estimation Using Proposed Distance Function

Abstract

Calibration estimation is a method of adjusting the original design weights in survey sampling to improve estimates. It uses calibrated weights that are determined to minimize a given distance measure to the original design weights while satisfying a set of constraints related to the auxiliary information. In this paper, a distance function is proposed. Using the proposed distance function, a calibration estimator of the population mean in stratified sampling is derived. The calibrated weights are determined by minimizing the proposed distance function subject to the constraint on the mean auxiliary information, using Lagrange Multiplier Technique. A numerical example is presented to illustrate the application and computational details of the proposed calibration estimator. A simulation study, based on a real population is also carried to investigate the efficiency of the proposed calibration estimator. The study reveals that the calibration estimator developed using the proposed distance function is more efficient than the estimators developed using the Chi-square distance.