Adaptive drift estimation for nonparametric diffusion model

• 成果类型: Article
• 署名作者: Spokoiny, VG
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1015951999
• 发表日期: 2000
• 页码: 815-836
• 关键词: variance-function estimation; spatial adaptation; regression; Wavelets

摘要

We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.