On a local uniform bootstrap validity |
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Authors: | T Bednarski & W Florczak |
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Institution: | Institute of Mathematics, Polish Academy of Sciences, Wrocław, and Institute of Mathematics, Pedagogical University, Zielona Góra,;Institute of Mathematics, Polish Academy of Sciences, Wrocław |
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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. |
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Keywords: | robust estimation von Mises calculus |
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