Using past sample means in exponential ratio and regression type estimators under a simple random sampling

Abstract Statistical sampling commonly employs auxiliary variables for the selection and estimation phases to improve efficiency of the estimators. However, existing estimators like ratio and product types display limitations under specific conditions. Regression-type estimators, known for their unbiasedness and efficiency, rely solely on current sample information. This highlights the need for more effective estimators capable of leveraging both past and current sample means to improve accuracy and applicability across diverse datasets. In this study, we introduce two novel memory-type estimators, drawing inspiration from Noor-ul-Amin's (2020) approach, which integrates past and current sample information using Hybrid Exponentially Weighted Moving Averages (HEWMA), particularly effective for time-based surveys. Through simulation studies and real data examples, we evaluate the performance of our estimators and identify crucial shortcomings in previous memory-type estimator studies. Furthermore, we highlight significant deficits in previous studies, particularly concerning the impact of sample sizes based on past means, correlation, number of past means, weight parameters and initial values of EWMA and HEWMA algorithms, and the distribution shape of the data on estimator efficiency. Our findings underscore the importance of parameter selection in HEWMA, a greater number of past means, and the significance of past sample sizes for optimizing the performance of the proposed memory-type estimators. By integrating HEWMA, our approach enhances the efficiency and applicability of these estimators, addressing essential gaps in the existing literature and laying the groundwork for more robust and efficient estimation techniques for future studies that use mean.