statsmodels.nonparametric.kernel_density.KDEMultivariate

class statsmodels.nonparametric.kernel_density.KDEMultivariate(data, var_type, bw=None, defaults=<statsmodels.nonparametric._kernel_base.EstimatorSettings object>) [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:

data (list 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_type (str) – 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'. bw (array_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 defaults (EstimatorSettings instance, optional) – The default values for (efficient) bandwidth estimation.

bw

array_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.