ASYMPTOTIC EQUIVALENCE OF NONPARAMETRIC DIFFUSION AND EULER SCHEME EXPERIMENTS

• 成果类型: Article
• 署名作者: Genon-Catalot, Valentine; Laredo, Catherine
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Universite Paris Saclay; INRAE; Universite Paris Saclay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); INRAE; INRAE; Universite Paris Cite; Universite Paris Saclay
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1216
• 发表日期: 2014
• 页码: 1145-1165
• 关键词: statistical equivalence; DENSITY-ESTIMATION; white-noise; regression; nonequivalence; approximation; volatility; models; GARCH

摘要

We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived. The impact of these equivalence results is that it justifies the use of the Euler scheme instead of the discretized diffusion process for inference purposes.