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On a local uniform bootstrap validity

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  • T. Bednarski
  • W. Florczak

Abstract

Some relations between smoothness of statistical functionals and locally uniform validity of Efron's bootstrap for the estimators generated by the functionals are studied. It is shown that the Fréchet differentiability easily implies the locally uniform bootstrap validity. In an important example of empirical median it is indicated that indeed stronger regularity conditions are necessary to make the bootstrap a very reliable tool. It is also shown that a smoothing method based on Huber's M‐estimation applied to the median may lead to an improved simple bootstrap there.

Suggested Citation

  • T. Bednarski & W. Florczak, 1999. "On a local uniform bootstrap validity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(1), pages 111-121, March.
    • Handle: RePEc:bla:stanee:v:53:y:1999:i:1:p:111-121
    DOI: 10.1111/1467-9574.00101
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