The effect of correlated errors on the performance of local linear estimation of regression function based on random functional design

Karim Benhenni (), Ali Hajj Hassan () and Yingcai Su ()
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Karim Benhenni: Université Grenoble Alpes, UMR 5224 CNRS
Ali Hajj Hassan: Université Grenoble Alpes, UMR 5224 CNRS
Yingcai Su: Missouri State University

Statistical Papers, 2024, vol. 65, issue 6, No 3, 3395-3423

Abstract: Abstract This article considers the problem of nonparametric estimation of the regression function $$r$$ r in a functional regression model $$Y = r(X) +\varepsilon $$ Y = r ( X ) + ε with a scalar response Y, a functional explanatory variable X, and a second order stationary error process $$\varepsilon $$ ε . Under some specific criteria, we construct a local linear kernel estimator of $$r$$ r from functional random design with correlated errors. The exact rates of convergence of mean squared error of the constructed estimator are established for both short and long range dependent error processes. Simulation studies are conducted on the performance of the proposed simple local linear estimator. Examples of time series data are considered.

Keywords: Local linear kernel estimation; Functional random design data; Nonparametric regression function; Short and Long memory error processes; OU and ARFIMA processes (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01523-z

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