NONPARAMETRIC DRIFT ESTIMATION FOR IID PATHS OF STOCHASTIC DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Comte, Fabienne; Genon-Catalot, Valentine
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1933
• 发表日期: 2020
• 页码: 3336-3365
• 关键词: asymptotic statistical equivalence; maximum-likelihood-estimation

摘要

We consider N independent stochastic processes (X-i(t), t is an element of [0, T]), i = 1, ..., N, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval [0, T] where T is fixed. We study nonparametric estimation of the drift function on a given subset A of R. Projection estimators are defined on finite dimensional subsets of L-2 (A, dx). We stress that the set A may be compact or not and the diffusion coefficient may be bounded or not. A data-driven procedure to select the dimension of the projection space is proposed where the dimension is chosen within a random collection of models. Upper bounds of risks are obtained, the assumptions are discussed and simulation experiments are reported.