A Class of Estimators for Estimating the Population Mean and Variance Using Auxiliary Information Under Adoptive Cluster Sampling in Sample Surveys

For estimating the mean of finite population using information on an auxiliary variable we define the classes of estimators under adoptive cluster sampling in this paper. Expressions for their biases and mean squared errors are obtained under large sample approximation. The minimum mean squared errors of each class of estimators are also given. A similar class of estimators is defined for the variance of the estimator of the mean. A condition is obtained under which the proposed class of estimators of the variance of the estimator is minimum.