In trying to figure out if this problem I’m working on has been addressed by the statistics community, I found myself forming Google queries on “semiparametric Gaussian estimation.” The problem I’m looking at is the following. Suppose X(t) is an iid Gaussian vector. I get to observe Y(t) = A(t) X(t) + W(t) where W(t) is an iid Gaussian vector of noise and A(t) is a matrix-valued random variables taking values in a finite set, iid across time. I want to form a minimum mean-squared error (MMSE) estimate of X(t) from Y(t). If A(t) is known at all times t then this is easy since I can make a linear estimator for each value that A(t) can take. Instead, I’ll make the crazy assumption that the estimator has to be linear and designed off-line (i.e. not data dependent), and that the distribution p(A) is not known. What’s the best estimator and worst-case error?

In my searching the web, however, I turned up some crazy things on long memory parameters in nonstationary time series. I also came across the term kriging, which looked like a typo for something. Instead, it really means Gaussian process regression — yet another instance of jargon standing in the way of understanding. Unfortunately, I don’t think it’s quite what I want. Back to the ol’ search engine…

0 thoughts on “kriging

  1. It’s extremely irresponsible of you to just “assume” that the estimator “has” to be linear. It’s people like you that let the terrorists know that they’re winning.

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