The notion of influence function was introduced by Hampel and it plays a crucial role for the 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 the 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
Robustness by generalized influence function : a new approach / M. Fini, D. La Torre - In: Mathematical and statistical methods in insurance and finance / [a cura di] C. Perna, M. Sibillo. - Milano : Springer Milan, 2007. - ISBN 978-88-470-0703-1. - pp. 113-120 (( convegno MAF 2006 : metodi matematici e statistici per le assicurazioni e la finanza tenutosi a Salerno nel 2006 [10.1007/978-88-470-0704-8].
Robustness by generalized influence function : a new approach
M. FiniPrimo
;D. La TorreUltimo
2007
Abstract
The notion of influence function was introduced by Hampel and it plays a crucial role for the 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 the 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
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
