Estimation of the noise covariance operator in functional linear regression with functional outputs

Christophe Crambes; Nadine Hilgert; Tito Manrique Chuquillanqui

doi:10.1016/j.spl.2016.02.006

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Estimation of the noise covariance operator in functional linear regression with functional outputs

Journal article

Open access

Peer reviewed

Estimation of the noise covariance operator in functional linear regression with functional outputs

Christophe Crambes, Nadine Hilgert and Tito Manrique Chuquillanqui

Statistics and Probability Letters, Vol.113, pp.7-15

06/2016

DOI: https://doi.org/10.1016/j.spl.2016.02.006

Abstract

Functional linear regression

Functional response

Noise covariance operator

estimation

statistique appliquée

bruit

probabilité

This work deals with the estimation of the noise in functional linear regression when both the response and the covariate are functional. Namely, we propose two estimators of the covariance operator of the noise. We give some asymptotic properties of these estimators, and we study their behavior on simulations.

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Title: Estimation of the noise covariance operator in functional linear regression with functional outputs
Creators - without role: Christophe Crambes - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Nadine Hilgert - Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie
Tito Manrique Chuquillanqui - Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie
Publication Details: Statistics and Probability Letters, Vol.113, pp.7-15
Identifiers: 9980156009311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Journal article
Local Fields: hal-01331242