Abstract
It is shown how the method of Fréchet differentiability can simplify the asymptotic derivations in an important range of robust inferential problems for stationary and related time series models. The uniform root-n consistency of the empirical distribution function for the Cramer von Mises norm under a weak mixing condition is indicated. Various regularity conditions naturally implemented and leading to the differentiability are discussed. A simulation study supplementing the theoretical discussion is included.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Bednarski, T. Fréchet differentiability in statistical inference for time series. Stat Methods Appl 19, 517–528 (2010). https://doi.org/10.1007/s10260-010-0143-y
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DOI: https://doi.org/10.1007/s10260-010-0143-y