new correlation-function estimator

My research tidbit for the day was a long conversation with Kate Storey-Fisher (NYU), in which we discussed our new estimator for the correlation function that can estimate vector (or tensor or higher order) quantities. That is, it doesn't have to estimate the correlation function in bins, it can estimate any aribtrary parameterized representation sensibly. This includes, say, a parameterization that is derivatives with respect to cosmological parameters. That would estimate the cosmological parameters directly from the positions of galaxies! It also includes, say, a fourier representation. That would estimate the correlation function and the power spectrum simultaneously! It also includes, say, dependencies of the correlation function on redshift or position, which would test cosmological growth of structure and cosmological homogeneity. Etc! I'm stoked.

In the course of the discussion we came up with a strong test of the estimator: An affine-invariance test: If we make an affine transformation of the model regressors, do we get the same results at the correlation-function level? That's a great test, and something we can do easily and now. If we don't pass, our estimator is just plain wrong!