Decision theoretic analysis of spherical regression

Spherical regression in a decision theoretic framework is examined, where the data is observed on S2 with the parameter space being SO(3). Bayes estimators are characterized under squared error loss on SO(3) as well as conditions under which the least squares estimator is a Bayes estimator with respect to the Haar prior. Under continuity conditions and the compactness of SO(3), a Bayes estimator is admissible. Thus the least squares estimator is admissible.