KDEMultivariate.imse()

statsmodels.nonparametric.kernel_density.KDEMultivariate.imse

KDEMultivariate.imse(bw) [source]

Returns the Integrated Mean Square Error for the unconditional 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.

See p. 27 in [R9] for details on how to handle the multivariate estimation with mixed data types see p.6 in [R10].

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 [R10] for mixed data types).

[R9]	(1, 2) Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007)

[R10]

(1, 2, 3) 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
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