, Volume 80, Issue 2, pp 261-268

Exact convergence rate of bootstrap quantile variance estimator

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Summary

It is shown that the relative error of the bootstrap quantile variance estimator is of precise order n -1/4, when n denotes sample size. Likewise, the error of the bootstrap sparsity function estimator is of precise order n -1/4. Therefore as point estimators these estimators converge more slowly than the Bloch-Gastwirth estimator and kernel estimators, which typically have smaller error of order at most n -2/5.