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Regression models with correlated errors based on functional random design

BENHENNI, Karim - Personal Name
HEDLI-GRICHE, Sonia - Personal Name
RachdI, Mustapha - Personal Name

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

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Regression models with correlated errors based on functional random design

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Classification	NONE
Content Type	E-Jurnal

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Subject(s)	Asymptotic distribution Random functional data Kernel estimator Mean squared error (MSE) Short and long memory process ARFIMA and Ornstein–Uhlenbeck process Negatively associated process
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Statement of Responsibility	Karim Benhenni 1, Sonia Hedli-Griche 2, Mustapha Rachdi 3

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