Addressing non-response and measurement errors in time-scaled surveys

Measurement and non-response errors significantly affect the accuracy of estimates. Measurement errors, from inaccurate data collection, distort variable relationships and bias results, while non-response errors, from missing data, lead to unrepresentative samples, especially when systematic. Both increase variability, reduce precision, and compromise conclusions, risking flawed decisions.To tackle these challenges, we have developed a generalized class of exponential estimators to enhance the accuracy of population mean estimation in time-scaled surveys. We analyzed the impact of measurement and non-response errors on accuracy by examining two scenarios: one where non-response affects only the study variable and another where it impacts both the study and auxiliary variables, with measurement error accounted for in both cases. We derive expressions for the bias and mean square error of the proposed estimator, considering the effects of measurement error and non-response, up to the first-order approximation. For time-scaled surveys, we compare its performance with several existing estimators. Extensive simulation studies demonstrate that the proposed estimator achieves greater efficiency in addressing these errors compared to current methods.