statsmodels.stats.correlation_tools.kernel_covariance¶
-
statsmodels.stats.correlation_tools.
kernel_covariance
(exog, loc, groups, kernel=None, bw=None)[source]¶ Use kernel averaging to estimate a multivariate covariance function.
The goal is to estimate a covariance function C(x, y) = cov(Z(x), Z(y)) where x, y are vectors in R^p (e.g. representing locations in time or space), and Z(.) represents a multivariate process on R^p.
The data used for estimation can be observed at arbitrary values of the position vector, and there can be multiple independent observations from the process.
- Parameters
- exogarray_like
The rows of exog are realizations of the process obtained at specified points.
- locarray_like
The rows of loc are the locations (e.g. in space or time) at which the rows of exog are observed.
- groupsarray_like
The values of groups are labels for distinct independent copies of the process.
- kernel
MultivariateKernel
instance
,optional
An instance of MultivariateKernel, defaults to GaussianMultivariateKernel.
- bwarray_like or scalar
A bandwidth vector, or bandwidth multiplier. If a 1d array, it contains kernel bandwidths for each component of the process, and must have length equal to the number of columns of exog. If a scalar, bw is a bandwidth multiplier used to adjust the default bandwidth; if None, a default bandwidth is used.
- Returns
A
real-valuedfunction
C
(x
,y
)that
returns
an
estimate
of
the
covariance
between
values
of
the
process
located
at
x
and
y.
References
- 1
Genton M, W Kleiber (2015). Cross covariance functions for multivariate geostatics. Statistical Science 30(2). https://arxiv.org/pdf/1507.08017.pdf