linearmodels.panel.covariance.HeteroskedasticCovariance¶

class linearmodels.panel.covariance.HeteroskedasticCovariance(y: ndarray, x: ndarray, params: ndarray, entity_ids: ndarray, time_ids: ndarray, *, debiased: bool = False, extra_df: int = 0)[source]¶

Covariance estimation using White estimator

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¶: (entity x time) by 1 stacked array of entity ids
time_ids: ndarray¶: (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

\[n^{-1}\hat{\Sigma}_{xx}^{-1}\hat{S}\hat{\Sigma}_{xx}^{-1}\]

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_df and n-df is replace by n-df-k if debiased is True.

Methods

`deferred_cov`()	Covariance calculation deferred until executed

Properties