Uncertainty Based Optimized Sampling Strategy for Population Mean Estimation under Correlated Measurement Errors

Accepted April 2026

Abstract

In sampling surveys and observational studies, the presence of correlated measurement errors (CME) under uncertainty can extremely distort the estimation of the population mean. The conventional estimators, which often assume independent and error-free measurements, may lose efficiency and lead to the biased conclusions in such complex situations. This article suggests an uncertainty based optimal class of estimator for the population mean under simple random sampling (SRS) that accounts for CMEs. Analytical properties of the proposed strategy are derived, including bias and mean squared error (MSE) expressions, which highlight the advantages of the proposed method over the adapted estimators. A simulation study is executed to evaluate the performance under different correlation patterns and uncertainty levels, showing the significant gains in efficiency and stability. The practical significance of the strategy is also illustrated through a real data application. The findings suggest that the uncertainty based optimized sampling strategy offers a reliable and efficient alternative for practitioners dealing with CMEs in survey sampling.