Efficient Estimation of Population Mean Using Robust Regression Methods in Outlier-Prone Data

In survey sampling, the outlier-prone data can severely affect the efficiency of traditional estimators of the population mean. This article proposes a class of estimators based on robust regression methods such as Hampel-M, Huber-M, Tukey-M, least trimmed squares, least median of squares, and Huber-MM, for efficient estimation of the population mean in outlier-prone datasets using simple random sampling (SRS). The proposed estimators are less sensitive to outliers and provide improved statistical properties like lower bias and mean square error (MSE) in non-ideal conditions. Expressions for the bias and MSE of the proposed class are derived and efficiency comparisons are made with some well-known robust regression estimators. To support the theoretical findings, an empirical study is also conducted using both real and artificially generated datasets under various robust regression methods.