The answer to this question gave me an interesting idea. The part that interested me was a brief description of kriging concluded by
The way, kriging as usually practiced is not quite the same as least squares estimation, because Σ is estimated in a preliminary procedure (known as "variography") using the same data. That is contrary to the assumptions of this derivation, which assumed Σ was known (and a fortiori independent of the data). Thus, at the very outset, kriging has some conceptual and statistical flaws built into it. Thoughtful practitioners have always been aware of this and found various creative ways to (try to) justify the inconsistencies. (Having lots of data can really help.) Procedures now exist for simultaneously estimating Σ and predicting a collection of values at unknown locations. They require slightly stronger assumptions (multivariate normality) in order to accomplish this feat.
The question I had from this was is there a similar method for cokriging like how generalized spatial models are an improvement upon kriging? Basically a technique that doesn't assume anything on Sigma or mu and uses the secondary variate.
