Abstract
If the underlying distribution functionF is smooth it is known that the convergence rate of the standard bootstrap quantile estimator can be improved fromn −1/4 ton −1/2+ε, for arbitrary ε>0, by using a smoothed bootstrap. We show that a further significant improvement of this rate is achieved by studentizing by means of a kernel density estimate. As a consequence, it turns out that the smoothed bootstrap percentile-t method produces confidence intervals with critical points being second-order correct and having smaller length than competitors based on hybrid or on backwards critical points. Moreover, the percentile-t method for constructing one-sided or two-sided confidence intervals leads to coverage accuracies of ordern −1+ε, for arbitrary ε>0, in the case of analytic distribution functions.
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Janas, D. A smoothed bootstrap estimator for a studentized sample quantile. Ann Inst Stat Math 45, 317–329 (1993). https://doi.org/10.1007/BF00775817
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DOI: https://doi.org/10.1007/BF00775817