Adaptive global thresholding on the sphere

This work is concerned with the study of adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. Our estimates are built by means of a form of spherical wavelets, the so-called needlets, enjoying strong concentration properties in both harmonic and real domains. We establish the convergence rates of the $L^p$-risks of these estimates, focussing on their minimax properties and proving their optimality over a scale of nonparametric regularity function spaces, namely Besov spaces.