Improved Estimation of Population Variance Incorporating Auxiliary Information in the Presence of Measurement Errors

Sehar Khalid; Hina Manzoor; Arifa Jahangir; Fakhra Ishaq; Natasha Habib; Arsalan Khan; Saddaf Zahra

doi:10.63056/

Authors

Sehar Khalid Lecturer, Department of Business Administration, Iqra University Chak Shahzad Campus, Islamabad. Author
Hina Manzoor Lecturer, Department of Business Administration, Iqra University Chak Shahzad Campus, Islamabad Author
Arifa Jahangir Lecturer, Department of Mathematics Science BUITEMS, Quetta. Author
Fakhra Ishaq Visiting Faculty, Department of Statistic, Islamic International University Islamabad. Author
Natasha Habib Visiting Lecturer, Department of Statistics, PMAS, Arid Agriculture University, Rawalpindi. Author
Arsalan Khan Visiting Lecturer, Department of Statistics, PMAS, Arid Agriculture University, Rawalpindi. Author
Saddaf Zahra Visiting Lecturer, Department of Statistics PMAS Arid Agricultural University. Author

DOI:

https://doi.org/10.63056/

Keywords:

Population Variance, Post-Stratified Sampling, Auxiliary Variables, Measurement Error, Mean Squared Error (MSE), Robust Estimation, Survey Sampling, Efficiency Comparison

Abstract

This study proposes a new class of estimators for using two auxiliary variables under classical additive measurement error a common issue in survey data. While traditional estimators assume error post-stratified population variance -free auxiliary information, this work explicitly accounts for measurement error, deriving bias and mean squared error (MSE) up to the first order of approximation. The proposed estimators incorporate known population parameters (means, coefficients of variation, correlation) and are evaluated using two benchmark datasets: Murthy (1967) and Kadilar & Cingi (2006). Results in Tables 1 and 2 shows that ignoring measurement error inflates MSE, leading to overestimation or underestimation of variance. Efficiency comparisons confirm that existing and proposed estimators perform poorly under error contamination. The study highlights the critical impact of data quality on inference and underscores the need for error-corrected estimation methods and robust data collection practices in survey sampling.