In this paper, we di fferentiate between isotropic and hyperbolic wavelet bases in the context of multivariate nonparametric function estimation. The study of the latter leads to new phenomena and non trivial extensions of univariate studies. In this context, we fi rst exhibit the limitations of...

We provide a novel treatment of the ability of the standard (wavelet-tensor) and of the hyperbolic (tensor product) wavelet bases to build nonparametric estimators of multivariate functions. First, we give new results about the limitations of wavelet estimators based on the standard wavelet...