statsmodels.nonparametric.kernel_density.KDEMultivariate.loo_likelihood

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

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:

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