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.
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Fini, M., La Torre, D. (2008). Generalized Influence Functions and Robustness Analysis. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods in Insurance and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-0704-8_15
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DOI: https://doi.org/10.1007/978-88-470-0704-8_15
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0703-1
Online ISBN: 978-88-470-0704-8
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