Robust Estimation of Variance Using Supplementary Information

Abstract

This study introduces robust exponential ratio-type estimators for finite population variance, incorporating the minimum covariance determinant (M.C.D.) and minimum volume ellipsoid (M.V.E.) robust covariance matrices in the context of simple random sampling. We utilize a first-order approximation to derive expressions for the bias and mean square error (M.S.E.) of these proposed estimators. Through a comprehensive review of existing literature, it is evident that these robust estimators outperform other alternatives in terms of efficiency. Both the M.C.D. and M.V.E. methods are known for their resilience to outliers, making them particularly effective when such anomalies are present in the data. Simulation studies and empirical results consistently demonstrate that the proposed robust exponential ratio-type estimators yield lower mean square errors compared to traditional estimators under simple random sampling. Additionally, the efficiency of these estimators is further validated through simulated studies and real-world data sets. Theoretical analysis and numerical evidence collectively affirm that the proposed class of estimators consistently outperforms competing methods across various scenarios.