Solved – Robust multivariate Gaussian fit in R

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I need to fit a generalized Gaussian distribution to a 7-dim cloud of points containing quite a significant number of outliers with high leverage. Do you know any good R package for this job?

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There's also mclust: http://www.stat.washington.edu/research/reports/2012/tr597.pdf http://cran.r-project.org/web/packages/mclust/index.html

One caution, though: mixture modelling in high dimensional space can get pretty CPU and memory intensive if your cloud of points is large. About four years ago I was doing a batch of 11-dimensional, 50-200K point data, and it was tending to run into 4-11GB of RAM and take up to a week to compute for each case (and I had 400). This is certainly possible, but can be a headache if you're using a shared compute cluster or have limited resources available.

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Solved – Fit a robust regression line using an MM-estimator in R

By default, the documentation indicates that rlm uses psi=psi.huber weights. Thus, if you want to use Tukey's bisquare, you need to specify psi=psi.bisquare. The default settings are psi.bisquare(u, c = 4.685, deriv = 0), which you can change as desired. For instance, possibly something like

rlm(x ~ y, method="MM", psi=psi.bisquare, maxit=50)

You may also want to investigate whether you should use least-trimmed squares (init="lts") to initialize your starting values. The default is to use least squares.

Solved – Robust parameter estimation for Exponentially modified Gaussian distribution

If it seems like most of the outliers are to the far right you could decide on a threshold including most of the datapoints to the left and censor all values to the right of that threshold. It would be akin to trimming but without introducing a bias. I don't know how you would run such an analysis in a classical statistics framework but it is "pretty easy" using Bayesian statistics

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Solved – Fit a robust regression line using an MM-estimator in R

Solved – Robust parameter estimation for Exponentially modified Gaussian distribution

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