On the adaptive estimation of a multiplicative separable regression function

We investigate the estimation of a multiplicative separable regression function from a bi-dimensional nonparametric regression model with random design. We present a general estimator for this problem and study its mean integrated squared error (MISE) properties. A wavelet version of this estimator is developed. In some situations, we prove that it attains the standard unidimensional rate of convergence under the MISE over Besov balls.