# Evaluating parametric vs non-parametric methods

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?

• Well, you could always simulate some datasets to study their performance over a parameter space that matches the one you find in your data? – abaumann May 29 '13 at 17:36

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!).