[SciPy-Dev] Expanding Scipy's KDE functionality

[Sturla Molden]

On 25.01.2013 16:28, josef.pktd at gmail.com wrote:

> If you just use a delta function,  you get the original data back, and
> we get the empirical distribution function, isn't it.I don't
> understand how this relates to digitizing the data.

What you get is a mathematical function that describes the data as an 
analog signal. The KDE can be seen as an anti-alias filter and an ADC.


> The pointwise variance of the density estimate is much smaller with a
> smooth, large bandwidth kernel, and the main task is to find the right
> bias-variance trade-off.

Bias-variance trade-off is the statistical perspective. The DSP 
perspective is selecting the appropriate low-pass filtering frequency. 
But numerically it is the same.

But what if the distribution has a sharp edge?

In DSP one often finds that wavelet shrinkage is better than low-pass 
filters at suppressing white noise from an arbitrary waveform. That for 
example applies to density estimation too. Wavelets can do better than KDE.


Sturla