[SciPy-Dev] Expanding Scipy's KDE functionality
Fri Jan 25 10:01:02 CST 2013
On 25.01.2013 16:28, firstname.lastname@example.org 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.
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