Minimum covariance determinant-based estimators for estimating population mean using two auxiliary variables

This study addresses the challenge of outliers in sample surveys, a common issue that can distort results and lead to inaccurate conclusions. To tackle this problem, researchers have developed various robust regression techniques including least trimmed squares, least median of squares, least absolute deviations, Huber’s, Hample’s and Tukey’s maximum likelihood estimators, and Huber’s maximum likelihood estimator for location and scale estimators. We propose a new approach: minimum covariance determinant-based ratio estimators for estimating the population mean in sample surveys. To assess the performance of the proposed minimum covariance determinant-based estimators, we derive their mean square error expressions and determine the conditions under which they surpass existing estimators in efficiency. To validate our theoretical findings, we conduct a numerical illustration using real-world data and perform simulations with R-Programme software. The results demonstrate that our method effectively handles outliers and improves the overall accuracy of survey-based estimations, making it a valuable tool for researchers working with sample survey data.