Estimation of mean considering the joint influence of measurement errors and non-response in two-phase sampling designs

Recently, a few studies have presented the problem of estimation of the mean for a finite homogenous population considering the joint influence of non-response and measurement errors and following the assumption that population mean of auxiliary variable is available. However, in real situations the population under observation may not be homogeneous and population mean of the auxiliary variable may also not be available. Therefore, in this study, we present new estimators which are the generalized form of the difference cum-exponential type estimator of the finite population mean in the presence of non-response and measurement errors in two phase simple random sampling and stratified random sampling. The expressions for mean square error and bias of the proposed estimators are shown under the first order approximation in each sampling design. Theoretically, it has been shown that the proposed estimators are more efficient than some existing estimators in both sampling designs. A numerical study has also been carried out using two different simulated populations under simple random sampling designs as well as under stratified random sampling design to support the theoretical results. Numerical results show that the proposed estimators perform more efficiently than some modified versions of the existing estimators in both sampling designs.