An Improved Exponential Ratio-Type Estimator with Two Auxiliary Variables in Double Sampling with Nonresponse

This research introduces a new exponential ratio-type estimator for estimating the population mean when survey data are affected by nonresponse. The proposed estimator utilizes two auxiliary variables within a double sampling framework in order to enhance estimation accuracy. Expressions for the mean squared error (MSE), coefficient of variation (CV), and relative efficiency (RE) of the estimator were derived. The performance of the estimator was assessed using numerical illustrations and compared with some existing estimators. The empirical results reveal that the proposed estimator yields smaller MSE and CV values while achieving higher relative efficiency across different subsampling rates at a 5% nonresponse level. The findings indicate that the integration of auxiliary variables through exponential adjustments leads to substantial improvement in estimator performance. Consequently, the proposed estimator provides a more reliable and efficient alternative for estimating population means in the presence of nonresponse.

Exponential ratio-type estimator, Nonresponse, Mean square error, Relative efficiency, Auxiliary information.

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