Generalized Memory-Type Estimators for Population Mean Under SRSWOR

Abstract

In classical survey sampling, the population mean is typically estimated using fixed observed values, often incorporating auxiliary information to improve precision. The primary objective of this study is to develop a family of memory-type estimators based on the Exponentially Weighted Moving Average (EWMA) technique for estimating the population mean. The proposed methodology exploits historical sample information through EWMA statistic, thereby enhancing the efficiency of estimation. A memory-based estimator incorporating auxiliary information is formulated under the framework of Simple Random Sampling Without Replacement (SRSWOR). The performance of the proposed family of estimators is evaluated through an extensive empirical investigation. The results demonstrate that the use of EWMA statistic significantly improves the precision of population mean estimation compared to conventional estimators. Furthermore, the efficiency of the proposed estimators can be controlled and optimized through appropriate selection of the smoothing parameter, δ. The practical applicability of the proposed methodology is illustrated using a real-world dataset.