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statsmodels.nonparametric.kernel_density.KDEMultivariate.loo_likelihood

KDEMultivariate.loo_likelihood(bw, func=<function <lambda> at 0x653c5f0>)[source]

Returns the leave-one-out likelihood function.

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

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.

Notes

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)

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