Bootstrapping Order Statistics with Variable Rank

Abstract

This work investigates the strong consistency of bootstrapping central and intermediate order statistics for an appropriate choice of re-sample size for known and unknown normalizing constants. We show that when the normalizing constants are estimated from the data, the bootstrap distribution for central and intermediate order statistics may be weakly or strongly consistent. A simulation study is conducted to show numerically how to choose the bootstrap sample size to give the best approximation of the bootstrapping distribution for the central and intermediate quantiles.