Generalized Power Transformation Estimators in Stratified Ranked Set Sampling using Auxiliary Information

Abstract

Auxiliary variable is commonly used in survey sampling to improve the precision of estimates. Whenever there is auxiliary information available, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. Stratified simple random sampling (SSRS) is used in certain types of surveys because it combines the conceptual simplicity of simple random sampling (SRS) with potentially significant gains in efficiency. It is a convenient technique to use whenever we wish to ensure that our sample is representative of the, population and also to obtain separate estimates for parameters of each sub domain of the population. Stratified Ranked Set Sampling combines the advantages of Stratification and Ranked set sampling (RSS) to obtain an unbiased estimator for the population mean, with potentially significant gains in efficiency. Under Stratified ranked set sampling scheme, we have suggested two general estimators using power transformation to estimate the population mean of the study variable. These methods are highly beneficial to the estimation based on Stratified Simple Random Sampling (SSRS).  The first order approximation to the bias and mean square error (MSE) of the proposed estimators are obtained. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in Stratified simple random sampling. A numerical illustration is also included to demonstrate the merits of the proposed estimator using SRSS over the corresponding estimators in SSRS.