The probability proportional to size (PPS) sampling method is frequently applied in engineering and industrial surveys when the auxiliary size measures can be obtained, and the population units are substantially heterogeneous. Nevertheless, classical PPS designs estimators are very susceptible to outliers and influential observations, which are common in engineering data because of measurement errors, extreme operating conditions, or structural variability. This research paper presents a powerful estimation method of the finite population mean using PPS sampling on auxiliary information. The proposed estimator has robust influence functions in the design-based PPS framework, enabling one to balance the impacts of extreme sample units by means of controlled weighting without breaking the sampling design on which it relies. Theoretical properties, such as design unbiasedness, consistency, and asymptotic variance of the estimator, are explored and compared with the traditional PPS estimators. Numerical findings show that the robust estimator significantly decreases the mean squared error compared to existing counterparts. The practical usefulness of the suggested methodology is demonstrated on an engineering dataset on the topic of operational performance measurements. Empirical findings prove the effectiveness of the robust estimator in delivering stable and reliable population estimates as opposed to the conventional PPS-based approaches. The results show that the concept of robustness remains critical in survey estimation when applied to engineering problems and can offer a convenient analysis device to analysts who need to work with heterogeneous and contaminated data. The proposed method provides an effective and flexible alternative to strong population estimation where the PPS sampling designs are applicable.
Citation: L. S. Diab, Norah D. Alshahrani, Majdah Mohammed Badr, Sohaib Ahmad. Robust population estimation under PPS sampling: An application to engineering data[J]. AIMS Mathematics, 2026, 11(5): 13008-13022. doi: 10.3934/math.2026535
The probability proportional to size (PPS) sampling method is frequently applied in engineering and industrial surveys when the auxiliary size measures can be obtained, and the population units are substantially heterogeneous. Nevertheless, classical PPS designs estimators are very susceptible to outliers and influential observations, which are common in engineering data because of measurement errors, extreme operating conditions, or structural variability. This research paper presents a powerful estimation method of the finite population mean using PPS sampling on auxiliary information. The proposed estimator has robust influence functions in the design-based PPS framework, enabling one to balance the impacts of extreme sample units by means of controlled weighting without breaking the sampling design on which it relies. Theoretical properties, such as design unbiasedness, consistency, and asymptotic variance of the estimator, are explored and compared with the traditional PPS estimators. Numerical findings show that the robust estimator significantly decreases the mean squared error compared to existing counterparts. The practical usefulness of the suggested methodology is demonstrated on an engineering dataset on the topic of operational performance measurements. Empirical findings prove the effectiveness of the robust estimator in delivering stable and reliable population estimates as opposed to the conventional PPS-based approaches. The results show that the concept of robustness remains critical in survey estimation when applied to engineering problems and can offer a convenient analysis device to analysts who need to work with heterogeneous and contaminated data. The proposed method provides an effective and flexible alternative to strong population estimation where the PPS sampling designs are applicable.
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L. S. Diab, Norah D. Alshahrani, Majdah Mohammed Badr, Sohaib Ahmad. Robust population estimation under PPS sampling: An application to engineering data[J]. AIMS Mathematics, 2026, 11(5): 13008-13022. doi: 10.3934/math.2026535
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