Asymptotic statistical equivalence for scalar ergodic diffusions

• 成果类型: Article
• 署名作者: Dalalyan, A; Reiss, M
• 署名单位: Sorbonne Universite; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0416-1
• 发表日期: 2006
• 页码: 248-282
• 关键词: Nonparametric regression; nonequivalence

摘要

For scalar diffusion models with unknown drift function asymptotic equivalence in the sense of Le Cam's deficiency between statistical experiments is considered under long-time asymptotics. A local asymptotic equivalence result is established with an accompanying sequence of simple Gaussian shift experiments. Corresponding globally asymptotically equivalent experiments are obtained as compound experiments. The results are extended in several directions including time discretisation. An explicit transformation of decision functions from the Gaussian to the diffusion experiment is constructed.