KDEMultivariate.loo_likelihood()

statsmodels.nonparametric.kernel_density.KDEMultivariate.loo_likelihood

KDEMultivariate.loo_likelihood(bw, func=<function KDEMultivariate.<lambda>>) [source]

Returns the leave-one-out likelihood function.

The leave-one-out likelihood function for the unconditional KDE.

Parameters:

Parameters:	bw: array_like The value for the bandwidth parameter(s). func: callable, optional Function to transform the likelihood values (before summing); for the log likelihood, use `func=np.log`. Default is `f(x) = x`.

bw: array_like

The value for the bandwidth parameter(s).

func: callable, optional

Function to transform the likelihood values (before summing); for the log likelihood, use func=np.log. Default is f(x) = x.

The leave-one-out kernel estimator of $f_{-i}$ is:

$f_{-i}(X_{i})=\frac{1}{(n-1)h} \sum_{j=1,j\neq i}K_{h}(X_{i},X_{j})$

where $K_{h}$ represents the generalized product kernel estimator:

$K_{h}(X_{i},X_{j}) = \prod_{s=1}^{q}h_{s}^{-1}k\left(\frac{X_{is}-X_{js}}{h_{s}}\right)$

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.nonparametric.kernel_density.KDEMultivariate.loo_likelihood.html