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Generalized influence functions and robustness analysis. (English) Zbl 1132.62035

Perna, Cira (ed.) et al., Mathematical and statistical methods in insurance and finance. Papers presented at the MAF2006 conference, Salerno, Italy, October 11–13, 2006. Milan: Springer (ISBN 978-88-470-0703-1/hbk). 113-120 (2008).
Summary: The notion of influence function was introduced by F. R. Hampel [J. Am. Stat. Assoc. 69, 383–393 (1974; Zbl 0305.62031)] and it plays a crucial role for important applications in robustness analysis. It is defined by the derivative of a statistic at an underlying distribution and it describes the effect of an infinitesimal contamination at point x on the estimate we are considering.
We propose a new approach which can be used whenever the derivative doesn’t exist. We extend the definition of influence function to nonsmooth functionals using a notion of generalized derivative. We also prove a generalized von Mises expansion.
For the entire collection see [Zbl 1124.91002].

MSC:

62G35 Nonparametric robustness
62G20 Asymptotic properties of nonparametric inference
62F35 Robustness and adaptive procedures (parametric inference)

Citations:

Zbl 0305.62031
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