linearmodels.system.covariance.HeteroskedasticCovariance¶
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class linearmodels.system.covariance.HeteroskedasticCovariance(x: list[ndarray], eps: Float64Array, sigma: Float64Array, full_sigma: Float64Array, *, gls: bool =
False, debiased: bool =False, constraints: LinearConstraint | None =None)[source]¶ Heteroskedastic covariance estimation for system regression
- Parameters:¶
- x: list[ndarray]¶
ndependent element list of regressor
- eps: Float64Array¶
Model residuals, ndependent by nobs
- sigma: Float64Array¶
Covariance matrix estimator of eps
- gls: bool =
False¶ Flag indicating to compute the GLS covariance estimator. If False, assume OLS was used
- debiased: bool =
False¶ Flag indicating to apply a small sample adjustment
- constraints: LinearConstraint | None =
None¶ 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.
Methods
Properties
Parameter covariance
Optional configuration information used in covariance
Error covariance