Regression models with correlated errors based on functional random design

Karim Benhenni (), Sonia Hedli-Griche () and Mustapha Rachdi ()
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Karim Benhenni: Université Grenoble Alpes
Sonia Hedli-Griche: Université Sétif
Mustapha Rachdi: Université Grenoble Alpes

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 1, No 1, 21 pages

Abstract: Abstract This paper deals with the study of the estimation of the functional regression operator when the explanatory variable takes its values in some abstract space of functions. The main goal of this paper is to establish the exact rate of convergence of the mean squared error of the functional version of the Nadaraya–Watson kernel estimator when the errors come from a stationary process under long or short memory and based on random functional data. Moreover, these theoretical results are checked through some simulations with regular (smooth) and irregular curves and then with real data.

Keywords: Random functional data; Kernel estimator; Mean squared error (MSE); Short and long memory process; Asymptotic distribution; ARFIMA and Ornstein–Uhlenbeck process; Negatively associated process; Primary 62G05; Secondary 62G07; 62G08; 62G35; 62G20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11749-016-0495-1

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