Abstract
Differentiability of statistical functionals is naturally linked to robustness. A robust estimator and a smooth one have frequently similar formal sense. Some notions of differentiability used in statistics are discussed in this context and it is concluded that Fréchet’s notion, for the supremum norm, gives a reasonable alternative. It is shown, under very mild assumptions, that estimators regular in a small model’s vicinity are asymptotically equivalent to M-estimators resulting from Fréchet differentiable functionals. A general result concerning questions of existence of the differentiable functionals for one-dimensional parametric models is also presented.
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Bednarski, T. (1994). Fréchet Differentiability and Robust Estimation. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_4
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DOI: https://doi.org/10.1007/978-3-642-57984-4_4
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