statsmodels.nonparametric.kernel_density.KDEMultivariate#

class statsmodels.nonparametric.kernel_density.KDEMultivariate(data, var_type, bw=None, defaults=None, *, rng=None)[source]#

Multivariate kernel density estimator

This density estimator can handle univariate as well as multivariate data, including mixed continuous / ordered discrete / unordered discrete data. It also provides cross-validated bandwidth selection methods (least squares, maximum likelihood).

Parameters:
datalist of ndarrays or 2-D ndarray

The training data for the Kernel Density Estimation, 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.

var_typestr

The type of the variables:

  • c : continuous

  • u : unordered (discrete)

  • o : ordered (discrete)

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

bwarray_like or str, optional

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 (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

KDEMultivariateConditional

Examples

>>> import statsmodels.api as sm
>>> nobs = 300
>>> np.random.seed(1234)  # Seed random generator
>>> c1 = np.random.normal(size=(nobs,1))
>>> c2 = np.random.normal(2, 1, size=(nobs,1))

Estimate a bivariate distribution and display the bandwidth found:

>>> dens_u = sm.nonparametric.KDEMultivariate(data=[c1,c2],
...     var_type='cc', bw='normal_reference')
>>> dens_u.bw
array([ 0.39967419,  0.38423292])

Methods

cdf([data_predict])

Evaluate the cumulative distribution function

imse(bw)

Returns the Integrated Mean Square Error for the unconditional KDE

loo_likelihood(bw[, func])

Returns the leave-one-out likelihood function

pdf([data_predict])

Evaluate the probability density function