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

See all articles by Danilo Matsuoka

Danilo Matsuoka

Research Group of Applied Microeconomics, Federal University of Rio Grande

Hudson Torrent

Universidade Federal do Rio Grande do Sul (UFRGS) - Department of Statistics

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

Matsuoka, Danilo and Torrent, Hudson, Convergence of the Local Linear Estimator for a Generalized Regression Function With Heterogeneous Dependent Functional Data (July 7, 2021). Available at SSRN: https://ssrn.com/abstract=3881570 or http://dx.doi.org/10.2139/ssrn.3881570

Danilo Matsuoka (Contact Author)

Research Group of Applied Microeconomics, Federal University of Rio Grande ( email )

Av. Itália, s/n - km 8 - Carreiros
Rio Grande, RS
Brazil

Hudson Torrent

Universidade Federal do Rio Grande do Sul (UFRGS) - Department of Statistics ( email )

Instituto de Matemática - UFRGS
Av. Bento Gonçalves, 9500 - Prédio 43-111 - Agrono
Porto Alegre, RS 91509-900
Brazil

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