Exact convergence rate of bootstrap quantile variance estimator

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