Improved Classes of Estimators for Population Mean Using Information on Auxiliary Character Under Double Sampling the Non-respondents

In this paper, improved classes of estimators have been proposed for estimating the population means of the study character using the information on auxiliary character and attribute in the presence of non-response on study character only and their properties are studied. The conditions for attaining the minimum mean square error of the proposed classes of estimators are also given. Further, the problem has been extended to the two phase sampling when the population proportion and mean of auxiliary character are not known. Two wider classes of generalized estimators under these conditions have been proposed and their properties are studied. The expressions of optimum sample size for first phase, second phase and sub-sampling fraction have been obtained in case of fixed cost as well as for fixed precision. Theoretical and empirical studies have been made with relevant estimators to show the efficiency of the proposed classes of estimators with real data set from census handbook published by Government of India.