Robust estimation of mean under probability proportional to size sampling: An application to radiation science and engineering data

The probability-proportional-to-size (PPS) sampling technique is widely used in radiation science and engineering to study problems in which the sampling elements vary significantly in size, activity, or exposure rate. The traditional design-based estimators of the population mean can be very unstable due to the presence of extreme values, heavy-tailed distributions and measurement uncertainties, which are typical of radiation data. Such problems may result in inflated variance and low inference uncertainty. This work constructs an effective estimator for population mean estimation using PPS sampling that explicitly accounts for influential observations without compromising important design-based characteristics. The combination of limited influence functions and weight correction mechanisms into the PPS design structure suggests a category of robust weighted estimators. Performance of estimators is measured using radiation science and engineering data. The proposed estimators will provide minimum mean squared error and a higher percentage relative efficiency. Empirical results confirm that the suggested estimators are more stable and reliable than traditional approaches. The suggested method thus offers an effective and statistically efficient mechanism for enhancing inference in surveys and engineering evaluations of radiation.