Calibration Approach for Estimation of Population Ratio under Double Sampling

Abstract

Ratio estimator is widely used survey estimation method for estimating the finite population mean (or total) using auxiliary variable which is linearly related to study variable. However, this method requires the availability of aggregate level population information for auxiliary variable which may not be always available. As a result, in many practical situations, the ratio method of estimation cannot be applied. Alternatively, the double (or two-phase) sampling approach is often applied in such cases. This paper develops the calibration approach based finite population ratio estimator using the double sampling. It is assumed that the ratio of the total of auxiliary variables is available for the first phase sample only. The expression for variance and estimator of the variance of the proposed estimator is also developed. In addition, optimum sample sizes for the first and second phase samples are also suggested for a fixed cost. Monte Carlo simulations based on real population show that the proposed estimator is efficient than the existing alternative.