statsmodels.nonparametric.kernel_density.KDEMultivariateConditional#

class statsmodels.nonparametric.kernel_density.KDEMultivariateConditional(endog, exog, dep_type, indep_type, bw, defaults=None, *, rng=None)[source]#

Conditional multivariate kernel density estimator

Calculates P(Y_1,Y_2,...Y_n | X_1,X_2...X_m) = P(X_1, X_2,...X_n, Y_1, Y_2,..., Y_m)/P(X_1, X_2,..., X_m). The conditional density is by definition the ratio of the two densities, see [1].

Parameters:
endoglist of ndarrays or 2-D ndarray

The training data for the dependent variables, used to determine the bandwidth(s). If a 2-D array, should be of shape (num_observations, num_variables). If a list, each list element is a separate observation.

exoglist of ndarrays or 2-D ndarray

The training data for the independent variable; same shape as endog.

dep_typestr

The type of the dependent variables:

  • c : Continuous

  • u : Unordered (Discrete)

  • o : Ordered (Discrete)

The string should contain a type specifier for each variable, so for example dep_type='ccuo'.

indep_typestr

The type of the independent variables; specified like dep_type.

bwarray_like or str

If an array, it is a fixed user-specified bandwidth. If a string, should be one of:

  • normal_reference: normal reference rule of thumb (default)

  • cv_ml: cross validation maximum likelihood

  • cv_ls: cross validation least squares

The bandwidths that are selected by one of the methods are kept in the range for which the kernels of the discrete variables are defined. The bandwidth of an unordered variable is at most (levels - 1) / levels, where levels is the number of distinct values of the variable, and the bandwidth of an ordered variable is less than 1. A user-specified bandwidth is used as given.

Changed in version 0.15.1: The bandwidths of discrete variables that are selected by one of the methods are bounded. They can have been outside the range of the kernels, so that the density estimate was not a probability mass function.

defaultsEstimatorSettings instance, optional

The default values for the efficient bandwidth estimation

rngint, array_like of int, numpy.random.Generator, or numpy.random.RandomState, optional

If rng is None, the legacy global (singleton) RandomState provided by numpy.random is used; this behavior is deprecated and will change to creating a new Generator using fresh entropy from the operating system in a future release. If rng is an int or array of ints, a new Generator is created, seeded with rng. If rng is already a Generator or RandomState instance, that instance is used.

Deprecated since version 0.15.0: In release 0.17.0 or after January 2028, whichever comes sooner, using None will initialize a new numpy.random.default_rng using system entropy.

Attributes:
bwarray_like

The bandwidth parameters

See also

KDEMultivariate

References

Examples

>>> import statsmodels.api as sm
>>> nobs = 300
>>> c1 = np.random.normal(size=(nobs,1))
>>> c2 = np.random.normal(2,1,size=(nobs,1))

>>> dens_c = sm.nonparametric.KDEMultivariateConditional(endog=[c1],
...     exog=[c2], dep_type='c', indep_type='c', bw='normal_reference')
>>> dens_c.bw   # show computed bandwidth
array([ 0.41223484,  0.40976931])

Methods

cdf([endog_predict, exog_predict])

Cumulative distribution function for the conditional density

imse(bw)

The integrated mean square error for the conditional KDE

loo_likelihood(bw[, func])

Returns the leave-one-out conditional likelihood of the data

pdf([endog_predict, exog_predict])

Evaluate the probability density function