| Abstract: | In this note we introduce a simple nonparametric estimator for densities on spheres and prove a speed of strong uniform convergence. The estimators are similar to the so-called naive estimators on Euclidean spaces. Due to the construction of the estimators, our main tool for proving this result appears to be a well-known exponential probability bound for empirical processes indexed by half-spaces. In the appendix we give a simple proof of this kind of inequality in a form suitable for our purposes. |
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