linearmodels.panel.covariance.HomoskedasticCovariance¶
-
class linearmodels.panel.covariance.HomoskedasticCovariance(y: ndarray, x: ndarray, params: ndarray, entity_ids: ndarray | None, time_ids: ndarray | None, *, debiased: bool =
False
, extra_df: int =0
)[source]¶ Homoskedastic covariance estimation
- Parameters:¶
- y: ndarray¶
(entity x time) by 1 stacked array of dependent
- x: ndarray¶
(entity x time) by variables stacked array of exogenous
- params: ndarray¶
variables by 1 array of estimated model parameters
- entity_ids: ndarray | None¶
(entity x time) by 1 stacked array of entity ids
- time_ids: ndarray | None¶
(entity x time) by 1 stacked array of time ids
- debiased: bool =
False
¶ Flag indicating whether to debias the estimator
- extra_df: int =
0
¶ Additional degrees of freedom consumed by models beyond the number of columns in x, e.g., fixed effects. Covariance estimators are always adjusted for extra_df irrespective of the setting of debiased
Notes
The estimator of the covariance is
\[s^2\hat{\Sigma}_{xx}^{-1}\]where
\[\hat{\Sigma}_{xx} = X'X\]and
\[s^2 = (n-df)^{-1} \hat{\epsilon}'\hat{\epsilon}\]where df is
extra_df
and n-df is replace by n-df-k ifdebiased
isTrue
.Methods
Covariance calculation deferred until executed
Properties
Estimated covariance
Model residuals
Covariance estimator name
Error variance