linearmodels.system.covariance.GMMHeteroskedasticCovariance¶
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class linearmodels.system.covariance.GMMHeteroskedasticCovariance(x: list[ndarray], z: list[ndarray], eps: Float64Array, w: Float64Array, *, sigma: ndarray | None =
None, debiased: bool =False, constraints: LinearConstraint | None =None)[source]¶ Covariance estimator for IV system estimation with homoskedastic data
- Parameters:¶
- x: list[ndarray]¶
List containing the model regressors for each equation in the system
- z: list[ndarray]¶
List containing the model instruments for each equation in the system
- eps: Float64Array¶
nobs by neq array of residuals where each column corresponds an equation in the system
- w: Float64Array¶
Weighting matrix used in estimation
- sigma: ndarray | None =
None¶ Residual covariance used in estimation
- constraints: LinearConstraint | None =
None¶ Constraints used in estimation, if any
Notes
The covariance is estimated by
\[(X'ZW^{-1}Z'X)^{-1}(X'ZW^{-1}\Omega W^{-1}Z'X)(X'ZW^{-1}Z'X)^{-1}\]where \(\Omega\) is the covariance of the moment conditions.
Methods
Properties
Parameter covariance
Optional configuration information used in covariance