A Theoretical Study of Generalized Auxiliary Variable Estimators for Finite Population Mean under Measurement Error and Non-Response

Muhammad Mubashir  Khan; Nadia  Idrees; Rabia  Munir; Hafiz Shabir  Ahmad

doi:10.63056/

Authors

Muhammad Mubashir Khan Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan Author
Nadia Idrees Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan Author
Rabia Munir Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan Author
Hafiz Shabir Ahmad Department of Mathematics and Statistics, At the University of Faisalabad, Pakistan Author

DOI:

https://doi.org/10.63056/

Keywords:

Auxiliary variable, bias, dual, exponential estimator, mean square error, non-sampling errors, measurement error, non-response

Abstract

This study proposes a generalized difference–cum–exponential type estimator for estimating the finite population mean under simple random sampling without replacement in the presence of measurement error and non-response. Auxiliary information is incorporated to improve estimation efficiency under a specific non-response scenario. Using first-order approximations, expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The optimum values of the involved constants are obtained by minimizing the MSE. Theoretical efficiency conditions are established to assess the performance of the estimator. The proposed estimator is analytically compared with existing estimators, including those of Hansen and Hurwitz (1946), Cochran (1977), Rao (1986), Bahl and Tuteja (1991), and Kumar and Bhougal (2011). Results based on MSE comparisons show that the proposed estimator outperforms the competing estimators under realistic survey conditions. The findings indicate that the proposed estimator is a reliable and efficient alternative for practical survey applications affected by measurement error and non-response.