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<p>The development of estimators that remain efficient under both normal and nonnormal conditions remains a critical challenge in statistical inference, particularly in the presence of data contamination and outliers. While several estimation methods have been proposed in the literature, limited attention has been given to constructing robust and highly efficient estimators within the broader class of long-tailed symmetric (LTS) distributions. This study addresses this gap by proposing new robust estimators for the population mean based on two distinct estimation approaches: Tiku’s modified maximum likelihood estimation (MMLE) and Lloyd’s generalized least squares estimation (GLSE). These methods are particularly suited to handle departures from normality and are applicable across the entire LTS family of distributions. The performance of the proposed estimators is assessed and compared with existing conventional estimators. Key performance indicators such as mean square errors (MSEs) and asymptotic relative efficiencies (REs) are computed using extensive Monte Carlo simulations. The results indicate that the proposed estimators outperform their traditional counterparts in small sample settings and demonstrate increasing efficiency and decreasing MSEs as sample size grows. A real-data application is also provided to illustrate the practical utility and robustness of the proposed estimators in real-world scenarios. This study contributes to the existing literature by offering a flexible and reliable estimation strategy that enhances inference in settings characterized by long-tailed behavior and nonnormality.</p>

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Efficient and Robust Estimators for the Population Mean of Non-normally Distributed and Contaminated Data

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • Aamir Majeed Chaudhary,
  • Aamir Sanaullah,
  • Muhammad Hanif,
  • Iram Saleem,
  • Prayas Sharma

摘要

The development of estimators that remain efficient under both normal and nonnormal conditions remains a critical challenge in statistical inference, particularly in the presence of data contamination and outliers. While several estimation methods have been proposed in the literature, limited attention has been given to constructing robust and highly efficient estimators within the broader class of long-tailed symmetric (LTS) distributions. This study addresses this gap by proposing new robust estimators for the population mean based on two distinct estimation approaches: Tiku’s modified maximum likelihood estimation (MMLE) and Lloyd’s generalized least squares estimation (GLSE). These methods are particularly suited to handle departures from normality and are applicable across the entire LTS family of distributions. The performance of the proposed estimators is assessed and compared with existing conventional estimators. Key performance indicators such as mean square errors (MSEs) and asymptotic relative efficiencies (REs) are computed using extensive Monte Carlo simulations. The results indicate that the proposed estimators outperform their traditional counterparts in small sample settings and demonstrate increasing efficiency and decreasing MSEs as sample size grows. A real-data application is also provided to illustrate the practical utility and robustness of the proposed estimators in real-world scenarios. This study contributes to the existing literature by offering a flexible and reliable estimation strategy that enhances inference in settings characterized by long-tailed behavior and nonnormality.