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<p>In survey sampling, the accurate estimation of the population mean is often challenged by the presence of outliers in the data. Traditional estimators may become inefficient or biased under such conditions. This study proposes a novel class of estimators for the population mean under simple random sampling (SRS) by incorporating robust regression methods that are less sensitive to outliers. The proposed estimators are formulated using robust regression methods, such as Hample-M, Huber-M, Tukey-M, Huber-MM, least trimmed squares (LTS), and least median of squares (LMS) to improve resistance against atypical observations while preserving efficiency under ideal conditions. The theoretical properties such as bias and mean square error (MSE) of the proposed estimators are examined. Through extensive simulation study and empirical application to real survey data, the proposed estimators demonstrate superior performance over the existing robust regression based estimators in terms of minimum relative mean square error (RMSE) and maximum relative efficiency (RE). The findings suggest that the proposed estimators provide a viable alternative for practitioners dealing with the data contaminated with outliers in sample surveys.</p>

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Novel class of population mean estimators based on robust regression methods

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月28日

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  • Anoop Kumar,
  • Renu Kumari,
  • Abdullah Mohammed Alomair,
  • Mohammed Ahmed Alomair

摘要

In survey sampling, the accurate estimation of the population mean is often challenged by the presence of outliers in the data. Traditional estimators may become inefficient or biased under such conditions. This study proposes a novel class of estimators for the population mean under simple random sampling (SRS) by incorporating robust regression methods that are less sensitive to outliers. The proposed estimators are formulated using robust regression methods, such as Hample-M, Huber-M, Tukey-M, Huber-MM, least trimmed squares (LTS), and least median of squares (LMS) to improve resistance against atypical observations while preserving efficiency under ideal conditions. The theoretical properties such as bias and mean square error (MSE) of the proposed estimators are examined. Through extensive simulation study and empirical application to real survey data, the proposed estimators demonstrate superior performance over the existing robust regression based estimators in terms of minimum relative mean square error (RMSE) and maximum relative efficiency (RE). The findings suggest that the proposed estimators provide a viable alternative for practitioners dealing with the data contaminated with outliers in sample surveys.