Error estimates for kernel and projection methods of recovering the orientation distribution function on $\mathrm{SO}(3)$

The orientation density function is recovered from a sample of orientations on the rotation group $\mathrm{SO}(3)$ of the three-dimensional Euclidean space. Sufficient conditions for the consistency of kernel and projection estimates in $L_2$, $L_1$, and $C$ are considered. Numerical results concerning the error estimation of projection methods over the basis of generalized spherical functions are given for normal distributions on $\mathrm{SO}(3)$.