Infinitesimal Robustness for Diffusions

• 成果类型: Article
• 署名作者: La Vecchia, Davide; Trojani, Fabio
• 署名单位: Universita della Svizzera Italiana
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm08383
• 发表日期: 2010
• 页码: 703-712
• 关键词: exchange-rates; estimators; models; inference

摘要

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.