Convergence of the Local Linear Estimator for a Generalized Regression Function With Heterogeneous Dependent Functional Data
29 Pages Posted: 8 Jul 2021 Last revised: 2 Sep 2021
Date Written: July 7, 2021
Abstract
In this study, we focus on a generalized nonparametric scalar-on-function regression model for heterogeneously distributed and strongly mixing data. We provide almost complete convergence rates for the local linear estimator of the regression function. We show that, under our conditions, the pointwise and uniform convergence rates are the same on a compact set. On the other hand, when the data is dependent, it is proved that the convergence rate can be slower than that of obtained for independent data. A simulation study shows the good performance and finite properties of the functional local linear estimator (FLL) in comparison to the local constant estimator (FLC). In addition, a one step ahead energy consumption forecasting exercise illustrates that the forecasts of the FLL estimator are significantly more accurate than those of the FLC.
Keywords: Almost complete convergence, Local linear estimator, Functional data, Mixing, Nonparametric regression
JEL Classification: C14, C13
Suggested Citation: Suggested Citation