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}
}
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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References

SHOWING 1-10 OF 26 REFERENCES

A note on bootstrapping the variance of sample quantile

SummaryLetmn, p denote thep-th quantile based onn observations and let λp denote the population quantile. In this paper consistency of the bootstrap estimate of variance of $$\sqrt n (m_{n,p} -

A Note on Bootstrapping the Sample Median

Abstract : Efron in this treatment of the bootstrap, discusses its use for estimation of the asymptotic variance of the sample median, in the sampling situation of independent and identically

On the estimation of the quantile density function

AN ESTIMATE OF THE ASYMPTOTIC STANDARD ERROR OF THE SAMPLE MEDIAN

Summary A method for estimating the asymptotic standard error of the sample median based on generalized least squares is outlined. The practical problems of implementing this new estimate along

A finite sample estimate of the variance of the sample median

Quantile processes with statistical applications

A Preliminary Study of Quantile Processes A Weak Convergence of the Normed Sample Quantile Process Strong Approximations of the Normed Quantile Process Two Approaches to Constructing Simultaneous

On the Best Obtainable Asymptotic Rates of Convergence in Estimation of a Density Function at a Point

In brief, by "rate of convergence" we will mean the rate which an tends to zero. For a continuum of different choices of the set C specified by various Lipschitz conditions on the kth partial

A Note on Estimating the Variance of the Sample Median

Abstract Estimation of the variance of the sample median based on small samples is discussed, and short tables are provided to facilitate calculation of the estimates.

Nonparametric Statistical Data Modeling

An approach to statistical data analysis which is simultaneously parametric and nonparametric is described, and density-quantile functions, autoregressive density estimation, estimation of location and scale parameters by regression analysis of the sample quantile function, and quantile-box plots are introduced.

Bootstrap Methods: Another Look at the Jackknife

We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X,