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 if debiased is True.

Methods

deferred_cov()

Covariance calculation deferred until executed

Properties

ALLOWED_KWARGS

DEFAULT_KERNEL

cov

Estimated covariance

eps

Model residuals

name

Covariance estimator name

s2

Error variance