Rate of Consistency Convergence for Nonparametric Pseudo-estimates with Functional Variables

Our main aim is to design a density pseudo-estimators(x) and mode estimators θn of nonparametric functional variables X.It is shown that the rate of consistency of the mode estimator for the density pseudo-estimator can be determined with some natural conditions.Indeed,our approach is to prove the rate of uniform convergence of the density pseudo-estimators of some nonparametric models in i.i.d.case and we establish the almost complete convergence rate of the mode estimators θn which extend the existing literature related results in i.i.d.case.