3.8.5.3.3.1.3. statsmodels.nonparametric.kernel_density.KDEMultivariate.imse¶
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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 [R37] for details on how to handle the multivariate estimation with mixed data types see p.6 in [R38].
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 [R38] for mixed data types).
References
[R37] (1, 2) Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) [R38] (1, 2, 3) Racine, J., Li, Q. “Nonparametric Estimation of Distributions with Categorical and Continuous Data.” Working Paper. (2000)