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Is M-estimation valid only for regression models or does it's working hold good for robust estimation of parameters in other statistical models? I understand that M-estimators are asymptotically normal for least squares models. Is it also true for any other model? I am guessing no, but do clarify.

What part of theory for M-estimation in regression holds for other non-regression models? Basically, am looking for if M-estimators are applied for non least-squares models. Every example I search for only gives M-estimators for least squares or nonlinear least-squares models.

user251385
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    A side note: apparently, it is not so easy to define just what a regression model is; see [this](http://stats.stackexchange.com/questions/173660/definition-and-delimitation-of-regression-model) thread. – Richard Hardy May 01 '16 at 08:12
  • Fair note, am looking for if M-estimators are applied for non least-squares models. Every example I search for only gives M-estimators for least squares or nonlinear least-squares models. – user251385 May 01 '16 at 16:11
  • @user251385 k-means minimizes sums of squares for clustering, you can minimize sum of squares for different problems. – Tim May 01 '16 at 16:49
  • @Tim my question is precisely whether M-estimation can be used in 'minimizing sum of squares for different problems' as you put it, in the presence of outliers? Are there any examples of M-estimation being done in such problems? – user251385 May 01 '16 at 17:21
  • Here: http://www2.cvl.isy.liu.se/ScOut/Publications/Papers/icpr06_felsberg_granlund_pchannels.pdf is a paper on M-estimation and clustering! which seems to answer your question. – kjetil b halvorsen May 01 '16 at 18:12
  • Does this paper use a distributional assumption or is it purely an optimization setting ? – user251385 May 01 '16 at 23:50

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