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Is there any function for $M$-estimation in multivariate linear regression model in R. I can estimate the $\beta$'s in my model by using the rlm() by rewriting the $y$-variables into one column but, I would like to use one function to get the $\beta$'s.

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Of possible interest: Link. – user10525 May 22 '12 at 11:19
@Procrastinator Your link does show someone who proves examples of robust estimation in R and specifically M-estimation. I think that qualifies as an answer to the question. Why don't you want to post it as an answer? – Michael Chernick May 22 '12 at 21:25
@MichaelChernick Thanks for your comment. I did not post it as an answer because I do not really understand what $M$-estimation means. I did a quick search by mere curiosity and found that link. – user10525 May 22 '12 at 21:29
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It looks like that link gives examples of univariate regression models using robust ($M$) estimation, but I think the question is about $M$-estimation for a multivariate dependent variable. – Macro May 23 '12 at 13:59

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The CRAN package rrcov specializes in robust estimation. The function covMest() gives the robust M-estimation of the covariance of a , but I could not find a specific function for multivariate regression.

If you already have a work around, you can write your own function to recode the data, call rml() and return the $\beta$s.

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That's not going to work in one important case: from the manual: 'The default initial estimate is the Minimum Volume Ellipsoid computed with CovMve'. Suppose there are some discrete variables in the design space. MVE's gonna chocke on them. e.g. there are situations where you would really want an convex M-estimator and not a re-descending one. – user603 Mar 20 at 14:17
@user603 Good job! It seems you looked into it deeper than I did. – gui11aume Mar 21 at 15:14
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I just found what you were looking for: it's implemented in the MNM package. Here is a link to the JoSS paper describing it.

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