Generalized Influence Functions and Robustness Analysis

Matteo Fini and Davide Torre ()
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Davide Torre: University of Milan

A chapter in Mathematical and Statistical Methods in Insurance and Finance, 2008, pp 113-120 from Springer

Abstract: Abstract The notion of influence function was introduced by Hampel 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.

Keywords: Robustness analysis; Influence function; Gross-error sensitivity; Prohorov distance; Qualitative robustness; Non-smooth analysis (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-0704-8_15

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DOI: 10.1007/978-88-470-0704-8_15

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