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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 [R6] for details on how to handle the multivariate estimation with mixed data types see p.6 in [R7].

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 [R7] for mixed data types).

References

[R6](1, 2) Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007)
[R7](1, 2, 3) Racine, J., Li, Q. “Nonparametric Estimation of Distributions with Categorical and Continuous Data.” Working Paper. (2000)

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