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The QFR estimator of total differs from traditional design-based estimators in that the weight assigned to each sample corporation is not based on its initial probability of selection. Instead, corporations in the enumerated industry are assigned weights equal to the ratio of the estimated total number of corporations in the type of industry at the time of enumeration to the number of sample corporations in that type of industry at the time of enumeration. Because the final QFR weight changes each quarter, the QFR estimator is referred to as a "variable weight estimator." There have been several investigations into the statistical properties of this variable weight estimator, but all prior studies have made simplifying assumptions. Instead, this workgroup attempted to account for all of the nuances of the QFR sample design and estimator via a Monte Carlo simulation study, comparing the existing estimator to several alternative variable weight estimators as well as to the Horvitz-Thompson estimator referred to by QFR as the "fixed weight estimator."
Ultimately, this study validated the current variable weight estimation method for QFR, showing it to have the lowest mean absolute error of the considered methods. Because of its sample design, the QFR has a coverage bias that is usually negative. The study found that none of the alternative variable weight estimators reduced the coverage bias compared to the current estimator, and that the coverage bias is approximately the same for the current estimator and the fixed weight estimator. Moreover, the quarter-to-quarter change estimates of sales constructed from the QFR variable weight estimates are more precise than the change estimates constructed from any of the considered alternative estimators, and the quarterly change in sales is a key economic statistic. Consequently, we recommend that QFR retain its current variable weight estimation methodology."
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