Calibration estimation approach for population ratio under adaptive cluster sampling

Abstract

Population ratio is one of the most commonly used statistics in official statistics, agriculture and agricultural-related fields. When interest is in the estimation of ratio for rare but highly aggregated geographically distributed population, adaptive cluster sampling (ACS) design is usually used (Dryver and Chang 2007). Under ACS design, neighbouring units are added to the sample if it satisfies a pre-determined criterion. ACS design allow observed values to trigger increased sampling effort during the survey. This intuitively appealing design can have lower variance than conventional designs. In many sampling survey situations, certain auxiliary information is often available and used for increasing the precision of estimator. Calibration approach given by Deville and Särndal (1992) is widely used technique for this purpose. In this article, calibration estimator of population ratio under adaptive sampling has been developed when auxiliary variables are known. The variance and the estimate of variance for these estimators are obtained. The statistical performance of the proposed calibration estimators of population ratio under ACS were evaluated through a simulation study based on real population data with respect to conventional Horvitz Thomson (HT) estimator of population ratio which do not utilize the auxiliary information. The results of the simulation study show that proposed calibration estimators are more efficient than conventional HT estimator of the population mean under ACS with respect to percentage Relative Root Mean Squared Error (%RRMSE).