📝 SummarXiv

Abstract

The notion of spherical $t$-designs has attracted interest in various areas of mathematics over the past decades. In this work, we consider spherical $t$-designs as the set of sampling points in non-parametric regression on spheres of arbitrary dimension. We show that the fixed design regression experiments defined this way are asymptotically equivalent, in the sense of Le Cam, to a sequence of Gaussian white noise experiments as the sample size tends to infinity. More precisely, global asymptotic equivalence is established for both Sobolev and Besov balls on the sphere. These results provide further support for the use of spherical $t$-designs as sampling points in non-parametric regression with spherical regressors.