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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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You will find links to at least four R packages for identifying multivariate outliers in the replies to a similar question at stats.stackexchange.com/questions/213/…. That might be a good start. –  whuber Jul 7 '11 at 13:51
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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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This sounds like a classic multivariate Gaussian Mixture Model. I think that the BayesM package might work.

Here are some multivariate Gaussian Mixture packages

  • bayesm: cran.r-project.org/web/packages/bayesm/index.html
  • mixtools: www.jstatsoft.org/v32/i06/paper
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