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Given data (as a vector) $y$, and a positive semi-definite matrix $W$ I would like to estimate $\mu$, $\tau$ and $\sigma$ via Maximum Likelihood in the following model:

$$y \sim N(\mu, \sigma I + \tau W). $$

Is there an off-the-shelf software solution for solving this problem in R?

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I decided to just write my own implementation. I have packaged it as an R package called NVC (Normal Variance Components) which can be downloaded at https://github.com/jsilve24/NVC

Its written in C++ using RcppEigen for speed. Uses closed form gradients to allow optimization with L-BFGS wrapped in RcppNumerical. It's fairly fast and should be scalable for most problems. Also documented and includes unit-testing.

Hopefully, this should be helpful to others.

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  • $\begingroup$ I am still interested if someone else has implemented this already in R. I find it strange if it wasn't already done. $\endgroup$
    – jds
    Commented Feb 7, 2019 at 20:05

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