Mean Estimation Using Memory-Type Estimators in Systematic Sampling for Time-Scaled Surveys

In this paper, we propose memory-type ratio, product, exponential ratio, and exponential product estimators based on an exponentially weighted moving average (EWMA) statistic for mean estimation in time-scaled surveys using systematic sampling. The approximate expressions for bias and mean squared error (MSE) of the proposed memory-type estimators are derived using Taylor and exponential series expansions up to the second order. Mathematical conditions are also established under which the memory-type ratio, product, exponential ratio, and exponential product estimators outperform their corresponding conventional estimators in terms of MSE. A simulation study is carried out to evaluate the performance of the proposed estimators compared to the conventional estimators. Additionally, real data application is also used to support the simulation findings. The results indicate that the proposed memory-type estimators have smaller MSEs than conventional estimators for time-scaled surveys using systematic sampling.