Covariance estimation for stochastic processes

Estimating the thing that is always given to you by oracles in statistics homework assignments. The meat of Gaussian process regression. A complement to Gaussian process simulation. Loosely speaking, if your stochastic distribution has only 2 free parameters and you can do mean and covariance estimation, you've done the whole thing.

To consider:

• relation to PCA.
• simulation of a field with a given covariance

Estimating the covariance, precision, concentration matrices of things. Turns about to be a lot more involved than estimating means in various ways and at various times. Long story.

• $\mathcal{H}$-matrix methods.

Wishart priors.

Sandwich estimators

For robust covariances of vector data. AKA Heteroskedasticity-consistent covariance estimators. Incorporating Eicker-Huber-White sandwich estimator, Andrews kernel HAC estimator, Newey-West and others.

https://eeecon.uibk.ac.at/~zeileis/papers/DAGStat-2007.pdf

Parametric covariance functions

For spatial statistics or other Cartesian-ish indexed random fields. I am told I should look up Matérn covariance matrices for a parametric covariance field.