# Exact convergence rate of bootstrap quantile variance estimator

@article{Hall1988ExactCR,
title={Exact convergence rate of bootstrap quantile variance estimator},
author={Peter Hall and Michael A. Martin},
journal={Probability Theory and Related Fields},
year={1988},
volume={80},
pages={261-268}
}
• Published 1 December 1988
• Mathematics
• Probability Theory and Related Fields
SummaryIt 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.

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