statsmodels.nonparametric.kernel_density.KDEMultivariate.imse¶

KDEMultivariate.imse(bw)[source]¶

Returns the Integrated Mean Square Error for the unconditional KDE.

Parameters :

bw: array_like :

The bandwidth parameter(s).

Returns :

—— :

CV: float :

The cross-validation objective function.

Notes

See p. 27 in [1] For details on how to handle the multivariate estimation with mixed data types see p.6 in [3]

The formula for the cross-validation objective function is:

$CV=\frac{1}{n^{2}}\sum_{i=1}^{n}\sum_{j=1}^{N} \bar{K}_{h}(X_{i},X_{j})-\frac{2}{n(n-1)}\sum_{i=1}^{n} \sum_{j=1,j\neq i}^{N}K_{h}(X_{i},X_{j})$

Where $\bar{K}_{h}$ is the multivariate product convolution kernel (consult [3] for mixed data types).