On a mapping approach to investigating the bootstrap accuracy |
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Authors: | Kani Chen Shaw-Hwa Lo |
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Institution: | (1) Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong , HK;(2) Department of Statistics, Columbia University, New York, NY 10027, USA, US |
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Abstract: | Summary. A simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting. It is demonstrated that
the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used Edgeworth
expansion approach may not be successfully applied. We then consider some examples to illustrate how this approach may be
used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the Gaussian approximation.
For the multivariate Kolmogorov–Smirnov statistic, we show the error of bootstrap approximation is as small as that of the
Gaussian approximation. For the multivariate kernel type density estimate, we obtain an order of the bootstrap error which
is smaller than the order of the error of the Gaussian approximation given in Rio (1994). We also consider an application
of the bootstrap accuracy for empirical process to that for the copula process.
Received: 23 June 1995 / In revised form: 18 June 1996 |
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Keywords: | Mathematics Subject Classification (1980): 60F17 62E20 |
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