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Infinitesimal robustness for diffusions

Contributors

La Vecchia, Davide; Trojani, Fabio

Published in

Journal of the American Statistical Association, vol. 105, no. 490, p. 703-712

Publication date

2010

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 processes
  • Eigenexpansion
  • Infinitesimal generator
  • Influence function
  • M-estimators
  • Saddle point approximation

UNIGE affiliation entities

Citation (ISO format)

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

Main files (1)

Article (Accepted version)

Identifiers

Journal ISSN

0162-1459
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Technical informations

Creation

08/09/2015 22:14:00

First validation

08/09/2015 22:14:00

Update

14/03/2023 23:36:39

Status update

14/03/2023 23:36:39

Last indexation

31/10/2024 01:14:16
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