Robust mean estimation in stratified sampling: A quantile regression approach

The presence of outliers can significantly reduce the reliability of conventional estimators, often resulting in biased estimation of the population mean. This challenge is particularly relevant in practical survey data, where irregular observations frequently occur. Although this issue is well-recognized, limited work has been done on population mean estimation under stratified random sampling when outliers are present, especially within a quantile regression framework. To address this gap, the present study introduces a new class of robust estimators based on quantile regression. The proposed estimators make use of non-conventional auxiliary information to improve estimation accuracy under a stratified random sampling scheme. By relying on quantile-based methods, the suggested approach provides greater resistance to the influence of outliers. The statistical properties of the proposed estimators are derived analytically, including measures of bias and mean squared error. In addition, their performance is examined through a real-life dataset. The findings indicate that the proposed estimators offer notable gains in efficiency and robustness compared to the adopted estimators, particularly in datasets affected by outliers.