Evaluating the impact of measurement errors in time-based surveys using a new class of memory type estimator

Time-based surveys are important tools in collecting data over time, but the presence of measurement errors (MEs) can significantly compromise the accuracy of the survey results. This article evaluates the impact of MEs in time-based surveys and introduces a new class of memory-type estimators designed to mitigate these errors using exponentially weighted moving average (EWMA) statistics. Unlike conventional estimators, which often assume constant error structures, the proposed memory-type estimator accounts for dynamic error processes and past and present observations in form of EWMA statistics, thus improving the precision of estimates over time. Through both theoretical analysis and empirical simulations, we demonstrate that the memory-type estimator provides superior performance in reducing bias and variance compared to the existing estimation methods under various error scenarios. This research contributes to the field of survey methodology by providing an advanced tool for more accurate time-based data analysis, particularly in contexts where MEs cannot be ignored. The findings highlight the potential for improving data reliability and informing policy decisions based on time-series survey data.