Kernel density estimator in an infinite-dimensional space with a rate of convergence in the case of diffusion process

摘要

We estimate the common probability density function of n i.i.d. observations at a fixed point, valued in an infinite-dimensional Banach space. A kernel estimator is proposed. Convergence in mean square is proved. Application to process of diffusion type is considered. (C) 2004 Elsevier Ltd. All rights reserved.