  This paper studies density estimation and regression analysis with
contaminated data observed on the unit hypersphere S^d. Our methodology and
theory are based on harmonic analysis on general S^d. We establish novel
nonparametric density and regression estimators, and study their asymptotic
properties including the rates of convergence and asymptotic distributions. We
also provide asymptotic confidence intervals based on the asymptotic
distributions of the estimators and on the empirical likelihood technique. We
present practical details on implementation as well as the results of numerical
studies.
