On adaptive wavelet estimation of the regression function and its derivatives in an errors-in-variables model
Christophe Chesneau · HAL (Le Centre pour la Communication Scientifique Directe) · 2010
We consider a regression model with errors-in-variables: $(Y,X)$, where $Y=f(Z)+\xi$ and $X=Z+W$. Our aim is to estimate the unknown regression function $f$ and its derivatives under mild assumptions on $\xi$ (only finite moments of order $2$ are required). To reach this goal, we develop a new adaptive wavelet estimator based on a hard thresholding rule. Taking the minimax approach under the mean integrated squared error over Besov balls, we prove that it attains a sharp rate of convergence.