linearmodels.system.covariance.HeteroskedasticCovariance¶
- class HeteroskedasticCovariance(x, eps, sigma, full_sigma, *, gls=False, debiased=False, constraints=None)[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
- 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
- x
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
Parameter covariance
Optional configuration information used in covariance
Error covariance