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KDEMultivariateConditional.imse()

statsmodels.nonparametric.kernel_density.KDEMultivariateConditional.imse

KDEMultivariateConditional.imse(bw) [source]

The integrated mean square error for the conditional KDE.

Parameters:

Parameters:	bw: array_like The bandwidth parameter(s).
Returns:	CV: float The cross-validation objective function.

bw: array_like

The bandwidth parameter(s).

Returns:

CV: float

The cross-validation objective function.

Notes

For more details see pp. 156-166 in [R22]. For details on how to handle the mixed variable types see [R23].

The formula for the cross-validation objective function for mixed variable types is:

$CV(h,\lambda)=\frac{1}{n}\sum_{l=1}^{n} \frac{G_{-l}(X_{l})}{\left[\mu_{-l}(X_{l})\right]^{2}}- \frac{2}{n}\sum_{l=1}^{n}\frac{f_{-l}(X_{l},Y_{l})}{\mu_{-l}(X_{l})}$

where

$G_{-l}(X_{l}) = n^{-2}\sum_{i\neq l}\sum_{j\neq l} K_{X_{i},X_{l}} K_{X_{j},X_{l}}K_{Y_{i},Y_{j}}^{(2)}$

where $K_{X_{i},X_{l}}$ is the multivariate product kernel and $\mu_{-l}(X_{l})$ is the leave-one-out estimator of the pdf.

$K_{Y_{i},Y_{j}}^{(2)}$ 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

[R22]

(1, 2) Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007)

[R23]

(1, 2) Racine, J., Li, Q. “Nonparametric Estimation of Distributions with Categorical and Continuous Data.” Working Paper. (2000)

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© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.nonparametric.kernel_density.KDEMultivariateConditional.imse.html