In survey studies, mean estimation is a main issue, and regression estimators that use conventional regression coefficients are the preferred options. However, traditional estimates may exhibit undesirable behaviour when outliers are present in the data. For such a situation, robust regression tools are utilized. In this paper, inspired by recent developments, some new finite population mean estimators are proposed by utilizing the robust regression tools under probability proportional to size sampling with replacement scheme. Two real datasets are applied for measuring the percentage relative efficiency of the proposed estimators with respect to the traditional ordinary least square regression mean and adapted estimators. It is found that the proposed estimators are more efficient than the considered estimators. In light of this, the proposed estimators may be valuable and almost certainly increase the chance of obtaining additional accurate population mean estimates in the presence of outliers.

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To cite this article: Mohamud Hussein Mohamud & Fartun Ahmed Mohamud (20 Jun 2025): Estimation of the mean using robust regression and probability proportional to size sampling, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2025.2516339

To link to this article: https://doi.org/10.1080/24754269.2025.2516339