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Bootstrap, wild bootstrap, and asymptotic normality
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  • Published: December 1992

Bootstrap, wild bootstrap, and asymptotic normality

  • Enno Mammen1 

Probability Theory and Related Fields volume 93, pages 439–455 (1992)Cite this article

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Summary

We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, W-6900, Heidelberg 1, Federal Republic of Germany

    Enno Mammen

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  1. Enno Mammen
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Additional information

This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 “Stochastische Mathematische Modelle”

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Cite this article

Mammen, E. Bootstrap, wild bootstrap, and asymptotic normality. Probab. Th. Rel. Fields 93, 439–455 (1992). https://doi.org/10.1007/BF01192716

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  • Received: 26 February 1990

  • Revised: 05 February 1992

  • Issue Date: December 1992

  • DOI: https://doi.org/10.1007/BF01192716

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Mathematics Subject Classification (1991)

  • 62 G 09
  • 62 G 05
  • 62 E 20
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