linearmodels.system.covariance.HeteroskedasticCovariance

class HeteroskedasticCovariance(x, eps, sigma, full_sigma, *, gls=False, debiased=False, constraints=None)

Heteroskedastic covariance estimation for system regression

Parameters:

xlist[ndarray]

ndependent element list of regressor

epsndarray

Model residuals, ndependent by nobs

sigmandarray

Covariance matrix estimator of eps

glsbool

Flag indicating to compute the GLS covariance estimator. If False, assume OLS was used

debiasedbool

Flag indicating to apply a small sample adjustment

constraints{None, LinearConstraint}

Constraints used in estimation, if any

Notes

If GLS is used, the covariance is estimated by

\[(X'\Omega^{-1}X)^{-1}\tilde{S}(X'\Omega^{-1}X)^{-1}\]

where X is a block diagonal matrix of exogenous variables and where \(\tilde{S}\) is a estimator of the model scores based on the model residuals and the weighted X matrix \(\Omega^{-1/2}X\).

When GLS is not used, the covariance is estimated by

\[(X'X)^{-1}\hat{S}(X'X)^{-1}\]

where \(\hat{S}\) is a estimator of the covariance of the model scores.

Attributes:

cov

Parameter covariance

cov_config

Optional configuration information used in covariance

sigma

Error covariance

Methods

Properties

cov	Parameter covariance
cov_config	Optional configuration information used in covariance
sigma	Error covariance