linearmodels.system.covariance.ClusteredCovariance¶

class linearmodels.system.covariance.ClusteredCovariance(x, eps, full_sigma, *, gls=False, debiased=False, constraints=None, clusters=None, group_debias=False)[source]

Heteroskedastic covariance estimation for system regression

Parameters:
x : list[ndarray]

ndependent element list of regressor

eps : ndarray

Model residuals, ndependent by nobs

sigma : ndarray

Covariance matrix estimator of eps

gls : bool

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

debiased : bool

Flag indicating to apply a small sample adjustment

constraints : {None, LinearConstraint}

Constraints used in estimation, if any

clusters : ndarray

Optional array of cluster id. Must be integer valued, and have shape (nobs, ncluster) where ncluster is 1 or 2.

group_debias : bool

Flag indicating whether to debias by the number of groups.

Notes

If GLS is used, the covariance is estimated by

$(X'\Omega^{-1}X)^{-1}\tilde{S}_{\mathcal{G}}(X'\Omega^{-1}X)^{-1}$

where X is a block diagonal matrix of exogenous variables and where $$\tilde{S}_{\mathcal{G}}$$ is a clustered 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

$(X'X)^{-1}\hat{S}_{\mathcal{G}}(X'X)^{-1}$

where $$\hat{S}$$ is a clustered estimator of the covariance of the model scores.

Methods

Properties

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