Robust Imputation for Population Mean Estimation with Outliers

This paper introduces three new imputation techniques and their corresponding point estimators to improve the estimation of the population mean under a Simple Random Sampling Without Replacement (SRSWOR) scheme. The proposed methods are designed to mitigate the combined negative effects of non-response and outliers, common nuisances in real-world data collection. We compare the large sample properties of our estimators with existing methods, including the mean, ratio, and estimators by Toutenburg et al., (2008), Kadilar and Cingi (2008), and Pandey et al., (2021). The theoretical properties are validated through empirical studies using both simulated data and real-world survey data. The results demonstrate the practical utility of our estimators in providing more accurate and robust estimations in scenarios such as public health surveys, market research, and economic studies where missing data and outliers are prevalent. The paper concludes with interpretations of the findings and provides recommendations for applying the proposed estimators in practical settings.