linearmodels.system.covariance.GMMKernelCovariance¶
-
class linearmodels.system.covariance.GMMKernelCovariance(x: list[ndarray], z: list[ndarray], eps: Float64Array, w: Float64Array, *, sigma: ndarray | None =
None
, debiased: bool =False
, constraints: LinearConstraint | None =None
, kernel: str ='bartlett'
, bandwidth: float | 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
- kernel: str =
'bartlett'
¶ Name of kernel to use. Supported kernels include:
”bartlett”, “newey-west” : Bartlett’s kernel
”parzen”, “gallant” : Parzen’s kernel
”qs”, “quadratic-spectral”, “andrews” : Quadratic spectral kernel
- bandwidth: float | None =
None
¶ Bandwidth to use for the kernel. If not provided the optimal bandwidth will be estimated.
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
Bandwidth used in estimation
Parameter covariance
Optional configuration information used in covariance
Kernel used in estimation