The integrated mean square error for the conditional KDE.
| Parameters : | bw: array_like :
|
|---|---|
| Returns : | CV: float :
|
Notes
For more details see pp. 156-166 in [1]. For details on how to handle the mixed variable types see [3].
The formula for the cross-validation objective function for mixed variable types is:
![CV(h,\lambda)=\frac{1}{n}\sum_{l=1}^{n}
\frac{G_{-l}(X_{l})}{\left[\mu_{-l}(X_{l})\right]^{2}}-
\frac{2}{n}\sum_{l=1}^{n}\frac{f_{-l}(X_{l},Y_{l})}{\mu_{-l}(X_{l})}](../_images/math/42483a42eb77b6550281f2ad307b4c5ef1de5f3c.png)
where
where 
is the multivariate product kernel and
is the leave-one-out estimator of the pdf.
is the convolution kernel.
The value of the function is minimized by the _cv_ls method of the GenericKDE class to return the bw estimates that minimize the distance between the estimated and “true” probability density.