A class of two phase sampling estimators for ratio of two population means using multi-auxiliary characters in the presence of non-response

In this paper, a class of two phase sampling estimators for estimating the ratio of two population means using multi-auxiliary characters with unknown population means has been proposed in presence of non-response. The asymptotic bias, mean square error and minimum mean square error of the proposed class of estimators have been obtained. The optimum values of the sample at the first and the second phases along with the sub-sampling fraction of the non-responding group have been determined for the fixed cost and for the specified precision. The efficiency of the proposed class of estimators has also been shown through the theoretical and empirical studies.