linearmodels.panel.covariance.HeteroskedasticCovariance

class HeteroskedasticCovariance(y, x, params, entity_ids, time_ids, *, debiased=False, extra_df=0)

Covariance estimation using White estimator

Parameters:

yndarray

(entity x time) by 1 stacked array of dependent

xndarray

(entity x time) by variables stacked array of exogenous

paramsndarray

variables by 1 array of estimated model parameters

entity_idsndarray

(entity x time) by 1 stacked array of entity ids

time_idsndarray

(entity x time) by 1 stacked array of time ids

debiasedbool

Flag indicating whether to debias the estimator

extra_dfint

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.

Attributes:

cov

Estimated covariance

eps

Model residuals

name

Covariance estimator name

s2

Error variance

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