Re: Which kernel to use for data in [0;1]?


yaroslavvb@xxxxxxxxx wrote:
> I need to learn density f(x):[0..1]->[0..1]
> In particular, x's are values generated by some unknown probability
> model.
> How would I do kernel density estimation in this setting?
>
> I had an idea to log-transform the data, make it symmetric around x=0
> by reflection, and use Gaussian kernel. Is this a typical approach to
> use in this setting?

I wouldn't be doing reflection.

What's wrong with transforming [0..1] to (-infinity..infinity)
directly?

There are any number of transformations, of which the logit is the most
obvious (logit(p) = log[p/(1-p)] ).

You can transform your density estimate back easily enough;
antilogit(x) = 1/[1+exp(-x)]
(though don't forget the Jacobian when you transform the density back)

Glen

.