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I am having a hard time finding comparisons between non-parametric and parametric methods, specifically for the task of density estimation (e.g. GMM vs using Dirichlet Processes).

More than tractability or running time, I am interested in their statistical performance on general datasets. Are there any known studies or papers on this topic?

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    $\begingroup$ Well, you could always simulate some datasets to study their performance over a parameter space that matches the one you find in your data? $\endgroup$ – abaumann May 29 '13 at 17:36
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I'm not an expert on this, but most text books on non-parametric methods have at least a short discussion on the 'root-n consistency' problem, see: http://www.ucl.ac.uk/~uctppca/aarhus/robinson.pdf

The basic result is that non-parametric estimators can't achieve a $O(n^{-1/2})$ order of convergence. Kernel methods, for example, give $O(n^{-2/5})$ convergence instead (using standard kernels and assumptions that is!).

I hope someone can give you a more specific answer to your question, but I think the general rule is that parametric models work better, when you can justify their assumptions.

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