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On a mapping approach to investigating the bootstrap accuracy
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  • Published: February 1997

On a mapping approach to investigating the bootstrap accuracy

  • Kani Chen1 &
  • Shaw-Hwa Lo2 

Probability Theory and Related Fields volume 107, pages 197–217 (1997)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong , , , , , , HK

    Kani Chen

  2. Department of Statistics, Columbia University, New York, NY 10027, USA, , , , , , US

    Shaw-Hwa Lo

Authors
  1. Kani Chen
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  2. Shaw-Hwa Lo
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Additional information

Received: 23 June 1995 / In revised form: 18 June 1996

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Chen, K., Lo, SH. On a mapping approach to investigating the bootstrap accuracy. Probab Theory Relat Fields 107, 197–217 (1997). https://doi.org/10.1007/s004400050083

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  • Issue Date: February 1997

  • DOI: https://doi.org/10.1007/s004400050083

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  • Mathematics Subject Classification (1980): 60F17
  • 62E20
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