A smoothed bootstrap estimator for a studentized sample quantile |
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Authors: | Daniel Janas |
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Institution: | (1) Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 6900 Heidelberg 1, Germany |
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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+, for arbitrary >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+, for arbitrary >0, in the case of analytic distribution functions. |
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Keywords: | Critical point confidence interval Edgeworth expansion kernel estimator percentile-t quantile smoothed bootstrap studentization |
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