Non linear wavelet estimation of regression derivatives based on biased data

Abstract

This paper considers non linear wavelet estimation on risk for the derivatives of regression function in Besov spaces based on biased data. It turns out that the convergence rate of non linear wavelet estimator keeps the same as Chaubey, Chesneau and Navarro’s linear estimator (Linear wavelet estimation of the derivatives of a regression function based on biased data, Communication in Statistics-Theory and Methods, 46: 9541-9556, 2017), when . However, the non linear estimator gets better if . On the other hand, our estimator is adaptive. Finally, our theory is illustrated with a simulation study.