Publication: Differentiable functionals and smoothed bootstrap.
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ISSN: 0020-3157 (print)
ISSN: 1572-9052 (online)
Publication date
1997-06
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Springer
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Abstract
The differentiability properties of statistical functionals have several interesting applications. We are concerned with two of them. First, we prove a result on asymptotic validity for the so-called smoothed bootstrap (where the artificial samples are drawn from a density estimator instead of being resampled from the original data). Our result can be considered as a smoothed analog of that obtained by Parr (1985, Stat. Probab. Lett., 3, 97-100) for the standard, unsmoothed bootstrap. Second, we establish a result on asymptotic normality for estimators of type Tn=T(fn) generated by a density functional T=T(f) fn being a density estimator. As an application, a quick and easy proof of the asymptotic normality of fn2 , (the plug-in estimator of the integrated squared density f2 ) is given.
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Keywords
Smoothed bootstrap, Differentiable statistical functionals, Bootstrap validity, Smoothed empirical process, Integrated squared densities
Bibliographic citation
Annals of the Institute of Statistical Mathematics, ( June 1997), 49(2), 355-370.