Open Access
2022 Estimating the conditional distribution in functional regression problems
Siegfried Hörmann, Thomas Kuenzer, Gregory Rice
Author Affiliations +
Electron. J. Statist. 16(2): 5751-5778 (2022). DOI: 10.1214/22-EJS2067

Abstract

We consider the problem of estimating the conditional distribution P(YA|X) of a functional data object Y=(Y(t):t[0,1]) in the space of continuous functions, given covariates X in a general space and assuming that Y and X are related by a functional linear regression model. Two estimation methods are proposed, based on either the empirical distribution of the estimated model residuals, or fitting functional parametric models to the model residuals. We show that consistent estimation can be achieved under relatively mild assumptions. We exemplify a general class of sets A specifying path properties of Y that are of interest in applications. The proposed methods are studied in several simulation experiments, and data analyses of electricity price and pollution curves.

Funding Statement

This research was partly funded by the Austrian Science Fund (FWF) [P 35520], and the Natural Science and Engineering Research Council of Canada [RGPIN-03723].

Acknowledgments

Parts of the results presented in this work were computed using the high-performance-computing resources of the Graz University of Technology IT Services. The authors wish to thank Mario Lang for his kind support, and Han Lin Shang for providing an implementation of the method described in Paparoditis and Shang [40].

Citation

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Siegfried Hörmann. Thomas Kuenzer. Gregory Rice. "Estimating the conditional distribution in functional regression problems." Electron. J. Statist. 16 (2) 5751 - 5778, 2022. https://doi.org/10.1214/22-EJS2067

Information

Received: 1 June 2022; Published: 2022
First available in Project Euclid: 3 November 2022

MathSciNet: MR4505381
zbMATH: 07633926
Digital Object Identifier: 10.1214/22-EJS2067

Subjects:
Primary: 62G05 , 62G20 , 62J05

Keywords: Empirical distribution , functional quantile regression , functional regression , functional time series , prediction sets

Vol.16 • No. 2 • 2022
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