statsmodels.nonparametric.kernel_density.KDEMultivariateConditional.imse¶
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KDEMultivariateConditional.
imse
(bw)[source]¶ The integrated mean square error for the conditional KDE.
Parameters: bw: array_like
The bandwidth parameter(s).
Returns: CV: float
The cross-validation objective function.
Notes
For more details see pp. 156-166 in [R15]. For details on how to handle the mixed variable types see [R16].
The formula for the cross-validation objective function for mixed variable types is:
where
where is the multivariate product kernel and is the leave-one-out estimator of the pdf.
is the convolution kernel.
The value of the function is minimized by the
_cv_ls
method of the GenericKDE class to return the bw estimates that minimize the distance between the estimated and “true” probability density.References
[R15] (1, 2) Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) [R16] (1, 2) Racine, J., Li, Q. “Nonparametric Estimation of Distributions with Categorical and Continuous Data.” Working Paper. (2000)