Transformed Memory Estimators for the Mean of Population in Time-Based Surveys

Incorporating ancillary information increases the precision and reliability of the estimators by reducing the sampling variability. Besides current ancillary information, past information available in different forms can also be utilized to get more accurate and stable estimators. The objective of the current research work is to improve the efficiency and precision of estimators of population mean in time-based surveys by using both current and past ancillary information. The aim of study is to design estimators which may minimize the sampling variability and mean square error (MSE) and improve the performance as compared with the existing classical and memory type ratio and product estimators. To obtain this aim, we have developed transformed memory-type ratio and product estimators by employing the exponentially weighted moving average (EWMA) statistic. The EWMA statistic is an important statistical tool that efficiently combines present and past information, thereby improving the overall performance of estimators. Under appropriate approximations, the expressions are obtained for the bias and MSE of the developed estimators. Moreover, mathematical conditions have been derived to show the superiority and dominance of the developed estimators over some of the available estimators existing in the literature. To validate the theoretical results, both empirical and simulation studies have been carried out. Empirical investigation is carried out on a real-world data set and simulation study is carried out on a population generated using R programing language. The outcomes of both the empirical and simulation analysis clearly demonstrate that the developed memory-type estimators outperform the existing estimators under appropriate conditions.