Data-driven Sobolev tests of uniformity on compact Riemannian manifolds

TL;DR

This paper introduces data-driven Sobolev tests for uniformity on compact Riemannian manifolds, which are invariant, consistent, and have well-characterized asymptotic null distributions.

Contribution

It proposes new invariant Sobolev tests that adapt to data and are valid for all alternatives on compact Riemannian manifolds.

Findings

Tests are invariant under isometries.

They are consistent against all alternatives.

Asymptotic null distributions are derived.

Abstract

Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are proposed. These tests are invariant under isometries and are consistent against all alternatives. The large-sample asymptotic null distributions are given.