Density estimation: from functional data to random fields

FORZANI, LILIANA; FRAIMAN, RICARDO; LLOP, PAMELA

Santiago de Chile - Chile

Congreso; III Congreso Latinoamericano y del Caribe de Matemáticos; 2009

Functional data and random fields are central topics inmodern statistical techniques. One of the most useful tools foranalyzing this kind of data is the density function. Due to thisimportance, in a first stage in this work we define anonparametric density estimator for functional data and under mildconditions we obtain strong consistency, strong order ofconvergence and asymptotic distribution. In addition we propose anonparametric classification rule based on local times (occupationmeasure). In a second stage we extend the definition of densityestimator to random fields. Since in this area physical constrainsmean that serious 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.