A GENERAL-APPROACH TO NONPARAMETRIC HISTOGRAM ESTIMATION

We note that some classical functional estimation problems may be redu ced to a general unique framework and study an estimator within this g eneral framework that reduces to the classical histogram type estimato rs in various examples presented. The convergence in probability and t he almost complete convergence of this general estimator are studied o btaining convergence conditions which reduce to the classical conditio ns in each case. Finally, this general framework provides conditions f or the convergence of the finite dimensional distributions of the asso ciated empirical process.