On local times, density estimation and supervised classification from functional data.

LLOP, PAMELA; FORZANI, LILIANA; FRAIMAN, RICARDO

JOURNAL OF MULTIVARIATE ANALYSIS

ELSEVIER INC

Año: 2011 vol. 102 p. 73 - 86

0047-259X

In this paper we define a $sqrt{n}$--consistent nonparametric estimator for the marginal density of an order one stationary process built up from a sample of iid continuous time trajectories. Under mild conditions we obtain strong consistency, strong orders of convergence and derive the asymptotic distribution of the estimator. We extend some of the results to the non-stationary case. We propose a nonparametric classification rule based on local times (occupation measure) and include some simulations studies.