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Qualitative robustness of von Mises statistics based on strongly mixing data. (English) Zbl 1416.62176

Summary: 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 [H. Zähle, Bernoulli 21, No. 3, 1412–1434 (2015; Zbl 1388.62071)] 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.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 1388.62071
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References:

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