Minimax optimal testing for structure of multivariate functions

We consider the problem of minimax hypothesis testing in the multivariate Gaussian White noise model. It is often reasonnable to assume that the underlying signal has some general structure (such as single index, additive...) and anisotropic smoothness. We will discuss the construction of test statistics for such structure based on hyperbolic (tensor product) wavelet coefficients. Then we will present their minimax properties and illustrate their performance through numerical experiments. 

This is a joint (and on-going) work wit Florent Autin, Gerda Claeskens and Christophe Pouet.