A Study on Domain Calibration Estimators under Two Stage Sampling Design

Abstract

The Calibration Approach proposed by Deville and Sarndal (1992) is one of the other techniques widely used for making efficient use of auxiliary information in survey estimation. Beyond the population parameters, there are sub-populations or domains for which estimates are needed to be generated now days. In this study, a domain calibration estimator for domain total were developed under two stage sampling design with assumptions of availability of auxiliary information at both PSU and SSU level of selection. The variance of the estimators and the corresponding variance estimators were also found. Both the proposed estimators were verified through limited simulation studies by generating an artificial population in R software. Various combinations of PSU and SSU sample sizes were drawn from each of the domains to draw the conclusions. Through the simulation study, it was found that all the proposed calibration estimators under two stage sampling design were performing at par with the Horvitz-Thompson estimator of the domain total under two stage sampling design with respect to the criteria of percent relative bias and performing consistently better than the HT estimator for the criteria of percent relative root mean square error.