Use of Auxiliary Variable to Improve the Efficiency of Exponential Type Estimator of Population Mean Under the Problem of Non-Response in Sample Surveys

This paper aims to propose an exponential-type estimator for estimating the population means under nonresponse problems in sample surveys within the framework of two-phase sampling. Additionally, the researcher examines some key properties of the proposed estimator, such as Mean Squared Error (MSE) and Minimum Mean Squared Error (MMSE). The MSE and Percent Relative Efficiency (PRE) are used as criteria to compare the efficiency of various estimators, both theoretically and in practical applications, using real data and through data simulation. The findings indicate that the proposed exponential estimator demonstrates greater efficiency than other estimators under the same conditions.