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Memory-type variance estimators using exponentially weighted moving average statistic in presence of measurement
Muhammad Nouman Qureshi1, Osama Abdulaziz Alamri2, Naureen Riaz3
1School of Statistics, University of Minnesota, Minneapolis, Minnesota, United States of America.
Abstract:
The present study suggested memory-type ratio and product estimators for variance estimation in the presence of measurement errors. We applied the exponentially weighted moving averages statistic which simultaneously utilizes the current and prior information for better estimation in surveys based on the time-scale. The expressions of approximate mean square errors of memory-type estimators are derived using Taylor series up to first order. Mathematical conditions are also obtained for which the suggested memory-type ratio and product estimators perform better than the conventional ratio and product estimators. The efficiency of the proposed estimators is observed using an extensive simulation study in the presence of measurement errors. A real data application is also carried out to support the mathematical expressions. From the results, it is shown that the use of prior sample information significantly increased the efficiency of the proposed estimators.
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