U.S. Department of Agriculture and National Institute of Statistical Sciences
When the weights associated with data collected from a finite population (i.e., a sample or a census) vary, estimators of the median are generally obtained from the (estimated) cumulative distribution function (CDF). Median estimators based on the CDF are often associated with sorting algorithms that asymptotically require 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 replicate methods, such as delete-a-group jackknife and bootstrap. Although the bootstrap approach has been shown to be more consistent than the leave-one-out jackknife when estimating the uncertainty of quantiles, it usually requires more iterations than the delete-a-group jackknife. More computationally efficient algorithms that also account 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.
