Nonparametric estimation of a surrogate density function in infinite-dimensional spaces

Abstract

A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate.