statsmodels.nonparametric.kernel_density.KDEMultivariateConditional.cdf¶

KDEMultivariateConditional.cdf(endog_predict=None, exog_predict=None)[source]¶

Cumulative distribution function for the conditional density.

Parameters:¶

endog_predictarray_like, optional

The evaluation dependent variables at which the cdf is estimated. If not specified the training dependent variables are used.

exog_predictarray_like, optional

The evaluation independent variables at which the cdf is estimated. If not specified the training independent variables are used.

Returns:¶

cdf_estarray_like

The estimate of the cdf.

Notes

For more details on the estimation see [2], and p.181 in [1].

The multivariate conditional CDF for mixed data (continuous and ordered/unordered discrete) is estimated by:

\[F(y|x)=\frac{n^{-1}\sum_{i=1}^{n}G(\frac{y-Y_{i}}{h_{0}}) W_{h}(X_{i},x)}{\widehat{\mu}(x)}\]

where G() is the product kernel CDF estimator for the dependent (y) variable(s) and W() is the product kernel CDF estimator for the independent variable(s).

References

[1]

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

[2]

Liu, R., Yang, L. “Kernel estimation of multivariate cumulative distribution function.” Journal of Nonparametric Statistics (2008)