terminology question

[gusl]

if you use a Gaussian kernel for density estimation, are you still in non-parametric-land?

Comments

[cdtwigg.livejournal.com]

Yes.

[gustavolacerda.livejournal.com]

This may be a trivial point, but it's easy to define a family of distributions parameterized by the set of data points, and the parameters of the Gaussian kernels.

Of course, you could also parameterize the family of computable distributions with the TM that produces each distribution...

[cdtwigg.livejournal.com]

But since you don't know a priori how many data points you'll be seeing, you can't make any statement about the dimensionality of the parameter space. Thus: the probability distribution your density estimator could potentially compute is completely arbitrary (could lie anywhere in an infinite-dimensional function space), and hence is not parametric.

[gustavolacerda.livejournal.com]

finite-dimensional: parametric
infinite-dimensional: nonparametric
?

If so, distributions over finite sets are always parametric. I think I can say something stronger here.

Amazing text..

[(Anonymous)]

thanks much, man