Infinitesimal robustness for diffusions

Davide La Vecchia, Fabio Trojani

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5 Citations (Scopus)

Abstract

We develop infinitesimally robust statistical procedures for the general diffusion processes. We first prove the existence and uniqueness of the times-series influence function of conditionally unbiased M-estimators for ergodic and stationary diffusions, under weak conditions on the (martingale) estimating function used. We then characterize the robustness of M-estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators. To compute these estimators, we propose a general algorithm, which exploits approximation methods for diffusions in the computation of the robust estimating function. Monte Carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real-data application.
Original languageEnglish
Pages (from-to)703 - 712
Number of pages10
JournalJournal of the American Statistical Association
Volume105
Issue number490
DOIs
Publication statusPublished - 2010
Externally publishedYes

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