Further Improving Finite Sample Approximation by Central Limit Theorems for Aggregate Efficiency

A simple yet easy to implement method is proposed to further improve the finite sample approximation by central limit theorems for aggregate efficiency. By adopt- ing the correction method in Simar and Zelenyuk (2020, EJOR), we further propose plugging the bias-corrected mean efficiency estimate rather than just mean efficiency estimate, into the variance estimator of aggregate efficiency. In extensive Monte-Carlo experiments, although our newly proposed method is found to have smaller coverages than the method using the true variance, it is found to have larger coverages across virtually all finite sample sizes and across dimensions than the original method in Simar and Zelenyuk (2018,OR) and the correction method in Simar and Zelenyuk (2020, EJOR). A real data set is employed to show the differences between these three methods in the estimated variance and the estimated confidence intervals.