Regression models with correlated errors based on functional random design

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...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2017-03, Vol.26 (1), p.1-21
Main Authors: Benhenni, Karim, Hedli-Griche, Sonia, Rachdi, Mustapha
Format: Article
Language:English
Subjects:
Convergence
Economics
Errors
Estimation bias
Estimators
Finance
Hypotheses
Insurance
Kernels
Management
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Original Paper
Regression
Simulation
Statistical Theory and Methods
Statistics
Statistics for Business
Studies
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Summary: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.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-016-0495-1