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Abstract:
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When the weights associated with data collected from a finite population using a sample or a census vary, estimators of the median are generally based on the estimated cumulative distribution function (CDF). Median estimators based on the CDF are often associated with sorting algorithms that require asymptotically O(n log n) operations. To improve the computational efficiency, alternative algorithms requiring O(n) operations are investigated and extended under complex sampling designs or, as in the case of a census, after weight adjustments. Furthermore, the uncertainty associated with median estimators is traditionally computed using subsampling methods, such as jackknife and bootstrap. Although the bootstrap approach has been shown to be more consistent than jackknife when estimating the uncertainty of quantiles, it usually requires many iterations than the delete-a-group jackknife. More computationally efficient algorithms that account also for the uncertainty introduced by calibration are desirable. This paper describes and compares several simulation studies that address both accuracy and timeliness of the median standard error.
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