M-estimators

[Marco-Congedo]

Hi,

referring to the list in issue #8 ,
i implemented the classical Tyler's M-estimator (1987) and the shrinked version proposed by Zhang and Wiesel (2016), with both the Ledoit & Wolf-type of shrinkage and the one advocated by the authors based on random matrix theory. The good news is that Zhang and Wiesel's estimator is pretty efficient, with a computational complexity comparable to the classical Tyler's M-estimator.

Are you interested in putting them in this package?

REFERENCES
David E. Tyler (1987)
A Distribution-Free M-Estimator of Multivariate Scatter
The Annals of Statistics, 15(1), 234-251.

Teng Zhang, Ami Wiesel (2016)
Automatic diagonal loading for Tyler's robust covariance estimator
IEEE Statistical Signal Processing Workshop (SSP), 1-5.

[tlienart]

Definitely, thanks!

[Marco-Congedo]

Nice, actually the two algorithms are stand-alone, they only requires LinearAlgebra.
Let me commit the .jl to start with, so that you can check and tell me how you see the support for those estimators should be done. Ok?

[mateuszbaran]

Thanks! I can look at your code and give some tips.

[Marco-Congedo]

OK, let me clean up a bit the code and i will commit.

[Marco-Congedo]

I committed. You will also find code for testing and benchmarking the algorithms as they stand. If you have any question do not hesitate to ask.

[mateuszbaran]

Thanks but where did you commit it?

[Marco-Congedo]

Sorry, now it should be OK.

[mateuszbaran]

Sorry but I can't find it, could you paste a link here?

[mateuszbaran]

OK, I see it now 👍 .

[Marco-Congedo]

Hello, any news on the addition of the Tyler's type M-estimator?

[mateuszbaran]

Sorry for this delay but it looks like it still requires a considerable amount of work. I don't currently need covariance estimation for anything so I keep prioritizing other tasks.