Learning from the Past: Extended-EWMA Driven Estimators for Population Mean in Survey Sampling
摘要
The precise estimation of population characteristics is a primary goal in survey sampling, especially when data variability and measurement errors may compromise the reliability of traditional estimators. This paper introduces a regression memory-type estimator and a generalized class of memory-type estimator for estimating the population mean, based on the Extended Exponentially Weighted Moving Average (EEWMA) technique, which incorporates both current and past observations with suitable weighting parameters. The suggested approach makes use of auxiliary information to enhance the efficiency of mean estimation and minimize bias, especially when population data show trends or fluctuations over time. The mean squared error (MSE) of the estimators are derived up to the first order of approximation. A simulation study is conducted to evaluate the performance of the memory-type estimators. The results show that the proposed generalized class of memory-type estimator is more efficient and robust across different correlation patterns.