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December, 1991 Rate of Convergence for the Wild Bootstrap in Nonparametric Regression
R. Cao-Abad
Ann. Statist. 19(4): 2226-2231 (December, 1991). DOI: 10.1214/aos/1176348394


This paper concerns the distributions used to construct confidence intervals for the regression function in a nonparametric setup. Some rates of convergence for the normal limit, its plug-in approach and the wild bootstrap are obtained conditionally on the explanatory variable $X$ and also unconditionally. The bound found for the wild bootstrap approximation is slightly better (by a factor $n^{-1/45}$) than the bounds given by the plug-in approach or the CLT for the conditional probability. On the contrary, the unconditional bounds present a different feature: the rate obtained when approximating by the CLT improves the one given by the plug-in approach by a factor of $n^{-8/45},$ while this last one performs better than the wild bootstrap approximation and the corresponding ratio is $n^{-1/45}.$ It should be mentioned that these two sequences, especially the last one, tend to zero at an extremely slow rate.


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R. Cao-Abad. "Rate of Convergence for the Wild Bootstrap in Nonparametric Regression." Ann. Statist. 19 (4) 2226 - 2231, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62038
MathSciNet: MR1135172
Digital Object Identifier: 10.1214/aos/1176348394

Primary: 62G05
Secondary: 62G99

Keywords: bootstrap , kernel smoothing , Nonparametric regression

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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