Abstract
In this manuscript, we have proposed a difference-type estimator for population mean under two-phase sampling scheme using two auxiliary variables. The properties and the mean square error of the proposed estimator are derived up to first order of approximation; we have also found some efficiency comparison conditions for the proposed estimator in comparison with the other existing estimators under which the proposed estimator performed better than the other relevant existing estimators. We show that the proposed estimator is more efficient than other available estimators under the two phase sampling scheme for this one example; however, further study is needed to establish the superiority of the proposed estimator for other populations.
Highlights
In survey sampling, the use of the auxiliary information at the estimation stage is widely used in order to obtain improved designs and the precision of an estimator of the unknown population parameter
When the knowledge of the auxiliary variable is used at the estimation stage, the ratio, product and regression methods of estimation are widely employed in these situations
The most important topic which is widely discussed in the various probability sampling schemes is the estimation of the population mean of the study variable
Summary
The use of the auxiliary information at the estimation stage is widely used in order to obtain improved designs and the precision of an estimator of the unknown population parameter. Let y and x be the study and the auxiliary variable with corresponding values yi and xi respectively for the i-th unit i = {1, 2, 3,..., N} defined in a finite population U with
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