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Qualitative robustness of von Mises statistics based on strongly mixing data

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  • Henryk Zähle

Abstract

In this article, the property of qualitative robustness is studied for von Mises statistics in the situation where the observations are not necessarily independent but are drawn from a strongly mixing sequence of identically distributed random variables. The notion of qualitative robustness is taken from “Zähle ( 2012 , submitted)” where Huber’s version of Hampel’s original definition was adapted to the case of dependent observations. The main result is illustrated by means of several examples including the sample variance, the sample Gini’s mean difference and the Cramér–von Mises statistic. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Henryk Zähle, 2014. "Qualitative robustness of von Mises statistics based on strongly mixing data," Statistical Papers, Springer, vol. 55(1), pages 157-167, February.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:157-167
    DOI: 10.1007/s00362-012-0478-6
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    References listed on IDEAS

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    1. Qiying, Wang, 1995. "The strong law of U-statistics with [phi]*-mixing samples," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 151-155, May.
    2. Beutner, Eric & Wu, Wei Biao & Zähle, Henryk, 2012. "Asymptotics for statistical functionals of long-memory sequences," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 910-929.
    3. Dehling, Herold & Wendler, Martin, 2010. "Central limit theorem and the bootstrap for U-statistics of strongly mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 126-137, January.
    4. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2012. "Qualitative and infinitesimal robustness of tail-dependent statistical functionals," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 35-47, January.
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