ADAPTIVE INVARIANT DENSITY ESTIMATION FOR ERGODIC DIFFUSIONS OVER ANISOTROPIC CLASSES

• 成果类型: Article
• 署名作者: Strauch, Claudia
• 署名单位: University of Mannheim
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1664
• 发表日期: 2018
• 页码: 3451-3480
• 关键词: functionals. ii. application; empirical processes theory; Oracle Inequalities; adaptation; selection

摘要

Consider some multivariate diffusion process X = (X-t)(t >= 0) with unique invariant probability measure and associated invariant density rho, and assume that a continuous record of observations X-T = (X-t)(0 <= t <= T) of X is available. Recent results on functional inequalities for symmetric Markov semi groups are used in the statistical analysis of kernel estimators (rho) over cap (T) = (rho) over cap (T) (X-T) of rho. For the basic problem of estimation with respect to sup-norm risk under anisotropic Holder smoothness constraints, the proposed approach yields an adaptive estimator which converges at a substantially faster rate than in standard multivariate density estimation from i.i.d. observations.