linearmodels.panel.covariance.HeteroskedasticCovariance¶
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class linearmodels.panel.covariance.HeteroskedasticCovariance(y: ndarray[tuple[int, ...], dtype[float64]], x: ndarray[tuple[int, ...], dtype[float64]], params: ndarray[tuple[int, ...], dtype[float64]], entity_ids: ndarray[tuple[int, ...], dtype[integer]], time_ids: ndarray[tuple[int, ...], dtype[integer]], *, debiased: bool =
False, extra_df: int =0)[source]¶ Covariance estimation using White estimator.
- Parameters:¶
- y: ndarray[tuple[int, ...], dtype[float64]]¶
(entity x time) by 1 stacked array of the dependent variable.
- x: ndarray[tuple[int, ...], dtype[float64]]¶
(entity x time) by variables stacked array of the exogenous variables.
- params: ndarray[tuple[int, ...], dtype[float64]]¶
Variables by 1 array of estimated model parameters.
- entity_ids: ndarray[tuple[int, ...], dtype[integer]]¶
(entity x time) by 1 stacked array of entity ids.
- time_ids: ndarray[tuple[int, ...], dtype[integer]]¶
(entity x time) by 1 stacked array of time ids.
- debiased: bool =
False¶ Flag indicating whether to debias the estimator. The default is False.
- 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. The default is 0.
- Raises:¶
ValueError – If the model has no residual degrees of freedom: the number of observations less
extra_df, and less the number of regressors ifdebiasedis True, is not positive.
Notes
The estimator of the covariance is
\[n^{-1}\hat{\Sigma}_{xx}^{-1}\hat{S}\hat{\Sigma}_{xx}^{-1}\]where
\[\hat{\Sigma}_{xx} = n^{-1}X'X\]and
\[\hat{S} = (n-df)^{-1} \sum_{i=1}^n \hat{\epsilon}_i^2 x_i'x_i\]where df is
extra_dfand n-df is replaced by n-df-k ifdebiasedisTrue.Methods
Covariance calculation deferred until executed.
Properties
Estimated covariance.
Model residuals.
Covariance estimator name.
Error variance.