A Fast Functional Locally Modeled Conditional Density and Mode for Functional Time-Series

Abstract

We study the asymptotic behavior of the nonparametric local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space. Under some general conditions on the mixing property of the data, we establish the pointwise almost-complete convergence, with rates, of this estimator. Moreover, we give some particular cases of our results which can also be considered as novel in the finite dimensional setting: Nadaraya-Watson estimator, multivariate data and the independent and identically distributed data case. On the other hand, this approach is also applied in time-series analysis to the prediction problem via the conditional mode estimation.