Density estimation: from functional data to random fields

FORZANI, LILIANA; FRAIMAN, RICARDO; LLOP, PAMELA

Maresías - Sao Sebatiao - SP - Brasil

Workshop; XIII Escola Brasileira de Probabilidade; 2009

NUMEC - IMPA

Functional data and random fields are central topics in modernstatistical techniques. One of the most useful tools for analyzingthis kind of data is the density function. Due to this importance,in a first stage in this work we define a nonparametric densityestimator for functional data and under mild conditions we obtainstrong consistency, strong order of convergence and asymptoticdistribution. In addition we propose a nonparametricclassification rule based on local times (occupation measure). Ina second stage we extend the definition of density estimator torandom fields. Since in this area physical constrains mean thatserious modelling can not be done using only independentsequences, we also consider dependents random fields which admitsa local time. In this context we study consistence and obtainlimits theorems.