References for Statistics on Manifolds and such?

[benfrantzdale]

For work and for fun, I've started thinking hard about statistics in non-Euclidean spaces. For example, how do you average angles or find the MLE of a point in SE(3)n given a collection of relative rigid-body transformations or a generalized median of several homographies?

I've found some interesting papers, but no great references... do you have any recommendations? I'd like to know more about Remannian geometry, to understand affine connections, and statistics in these spaces. Any book references would be appreciated.

Yay math!