Abstract

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The accuracy of the estimation is measured using pointwise risk. A data-driven procedure is proposed using kernel estimation with bandwidth selected via the Goldenshluger-Lepski approach. We demonstrate that the resulting estimator satisfies an oracle-type inequality and it is also shown to be adaptive over Hölder classes. This result constitutes a preliminary step toward the more general case in which the density of the explanatory variable is unknown. © 2025 Informa UK Limited, trading as Taylor & Francis Group.