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:¶

bwarray_like

The value for the bandwidth parameter(s).

funccallable, 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:

$$f_{-i}(X_i)=\frac{1}{(n-1)h}\sum _{j=1,j\ne i}{K}_h(X_i,X_j)$$

where $K_h$ represents the generalized product kernel estimator:

$$K_h(X_i,X_j)=\prod _{s=1}^q{h}_s^{-1}k\left(\frac{X_{is}-X_{js}}{h_s}\right)$$