statsmodels.nonparametric.kernel_density.KDEMultivariateConditional.cdf

method

KDEMultivariateConditional.cdf(endog_predict=None, exog_predict=None)

Cumulative distribution function for the conditional density.

Parameters

endog_predict: array_like, optional

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

exog_predict: array_like, optional

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

Returns

cdf_est: array_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(1,2)

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

2(1,2)

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