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On a local uniform bootstrap validity
Author(s) -
Bednarski T.,
Florczak W.
Publication year - 1999
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00101
Subject(s) - smoothness , estimator , smoothing , mathematics , simple (philosophy) , differentiable function , bootstrap aggregating , econometrics , statistics , mathematical analysis , philosophy , epistemology
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.