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Generalized Influence Functions and Robustness Analysis

In: Mathematical and Statistical Methods in Insurance and Finance

Author

Listed:
  • Matteo Fini

    (University of Milan)

  • Davide Torre

    (University of Milan)

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.

Suggested Citation

  • Matteo Fini & Davide Torre, 2008. "Generalized Influence Functions and Robustness Analysis," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 113-120, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-0704-8_15
    DOI: 10.1007/978-88-470-0704-8_15
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