statsmodels.nonparametric.kernel_density.KDEMultivariate.imse¶
- KDEMultivariate.imse(bw)[source]¶
Returns the Integrated Mean Square Error for the unconditional KDE.
- Parameters:
- bwarray_like
The bandwidth parameter(s).
- Returns:
- CV
float The cross-validation objective function.
- CV
Notes
See p. 27 in [1] for details on how to handle the multivariate estimation with mixed data types see p.6 in [2].
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 [2] for mixed data types).
References