Efficient Mean Estimation Using Repeated Measurements in PPS Sampling with Scientific Applications

Abstract

Research studies in many scientific disciplines need efficient estimation methods for estimating the parameters of quantitative variables, including, but not limited to, tensile strength, wind speeds, air quality, and temperature, etc. Statisticians employ a sampling design to get a random sample and estimate the population means based on the observed sample. If the units of a finite population have different selection probabilities, unequal probability methods of sample selection are used. The existing unequal probability sampling methods allocate probabilities proportional to size (PPS) to the population units by using a one-time measurement approach. Memory– type estimation methods, on the other hand, use multiple measurements and provide more precise estimates than the traditional estimators. This research study introduces a novel memory-type estimator using a PPS sampling design. Various properties of the suggested mean estimator are analyzed, and the efficiency conditions are derived. A few real-world data sets have been used from previous studies to evaluate the performance of the suggested and competing mean estimators. Our comparative study suggests that the suggested memory-based estimator performs much better than the competing estimators, which means that the suggested memory-type estimator is an appropriate estimator for application in real-life sample surveys.

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