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A smoothed bootstrap estimator for a studentized sample quantile

Research paper by Daniel Janas

Indexed on: 01 Jun '93Published on: 01 Jun '93Published in: Annals of the Institute of Statistical Mathematics



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.