Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We study a nonparametric regression model with circular responses in the presence of measurement errors in the covariates. The response variable takes values on the unit circle S1, while the predictors are observed through additive noise, leading to a statistical inverse problem. We consider both circular and linear predictors and propose a deconvolution-based estimator of the regression function adapted to the geometry of the circle. The regression function is recovered from two auxiliary functions p1 and p2 through the atan2 transformation. Under a non-degeneracy condition, the regularity of the regression function is inherited from that of these auxiliary functions. To avoid the need for prior knowledge of their smoothness, we develop a fully data-driven selection procedure. Under suitable regularity conditions on p1 and p2, we establish convergence rates for the pointwise risk, for both circular and linear predictors. The performance of the proposed estimators is investigated through numerical experiments.