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Regression models with correlated errors based on functional random design

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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.

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Authors and Affiliations

  1. LJK, UMR 5224 CNRS, Université Grenoble Alpes, Grenoble, France

    Karim Benhenni

  2. Université Sétif, Sétif, Algeria

    Sonia Hedli-Griche

  3. AGIM Team, AGEIS EA 7407, Université Grenoble Alpes, Grenoble, France

    Mustapha Rachdi

Authors
  1. Karim Benhenni
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  2. Sonia Hedli-Griche
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  3. Mustapha Rachdi
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Correspondence to Karim Benhenni.

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Benhenni, K., Hedli-Griche, S. & Rachdi, M. Regression models with correlated errors based on functional random design. TEST 26, 1–21 (2017). https://doi.org/10.1007/s11749-016-0495-1

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  • DOI: https://doi.org/10.1007/s11749-016-0495-1

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