Is there a good, modern treatment covering the various methods of multivariate interpolation, including which methodologies are typically best for particular types of problems? I'm interested in a solid statistical treatment including error estimates under various model assumptions.
Say we're sampling from a multivariate normal distribution with unknown parameters. What can we say about the standard error of the interpolated estimates?
I was hoping for a pointer to a general survey addressing similar questions for the various types of multivariate interpolations in common use.