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Infinitesimal robustness for diffusions

Published in Journal of the American Statistical Association. 2010, vol. 105, no. 490, p. 703-712
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.
Keywords Diffusion processesEigenexpansionInfinitesimal generatorInfluence functionM-estimatorsSaddle point approximation
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LA VECCHIA, Davide, TROJANI, Fabio. Infinitesimal robustness for diffusions. In: Journal of the American Statistical Association, 2010, vol. 105, n° 490, p. 703-712. doi: 10.1198/jasa.2010.tm08383 https://archive-ouverte.unige.ch/unige:75145

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Deposited on : 2015-09-13

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