Domain Mean Estimation Using Double Sampling with Non-Linear Cost Function in the Presence of Non Response

This paper describes theoretical estimation of domains mean using double sampling with a non-linear cost function in the presence of non-response. The estimation of domain mean is proposed using auxiliary information in which the study and auxiliary variable suffers from non-response in the second phase sampling. The expression of the biases and mean square errors of the proposed estimators are obtained. The optimal stratum sample sizes for given set of non-linear cost function are developed.