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Higher-Order Infinitesimal Robustness

Published in Journal of the American Statistical Association. 2012, vol. 107, no. 500, p. 1546-1557
Abstract Using the von Mises expansion, we study the higher-order infinitesimal robustness of a general M-functional and characterize its second-order properties. We show that second-order robustness is equivalent to the boundedness of both the estimator’s estimating function and its derivative with respect to the parameter. It implies, at the same time, (i) variance robustness and (ii) robustness of higher-order saddlepoint approximations to the estimator’s finite sample density. The proposed construction of second-order robust M-estimators is fairly general and potentially useful in a variety of relevant settings. Besides the theoretical contributions, we discuss the main computational issues and provide an algorithm for the implementation of second-order robust M-estimators. Finally, we illustrate our theory by Monte Carlo simulation and in a real-data estimation of the maximal losses of Nikkei 225 index returns. Our findings indicate that second-order robust estimators can improve on other widely applied robust estimators, in terms of efficiency and robustness, for moderate to small sample sizes and in the presence of deviations from ideal parametric models. Supplementary materials for this article are available online.
Keywords Generalized extreme value distributionM-estimatorRobustnessSaddlepointVon Mises Expansion
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LA VECCHIA, Davide, RONCHETTI, Elvezio, TROJANI, Fabio. Higher-Order Infinitesimal Robustness. In: Journal of the American Statistical Association, 2012, vol. 107, n° 500, p. 1546-1557. https://archive-ouverte.unige.ch/unige:28784

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Deposited on : 2013-07-05

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