linearmodels.system.covariance.HomoskedasticCovariance¶

class linearmodels.system.covariance.HomoskedasticCovariance(x: list[ndarray], eps: Float64Array, sigma: Float64Array, full_sigma: Float64Array, *, gls: bool = False, debiased: bool = False, constraints: LinearConstraint | None = None)[source]¶

Homoskedastic covariance estimation for system regression

Parameters:¶

x: list[ndarray]¶: List of regressor arrays (ndependent)
eps: Float64Array¶: Model residuals, ndependent by nobs
sigma: Float64Array¶: Covariance matrix estimator of eps
gls: bool = False¶: Flag indicating to compute the GLS covariance estimator. If False, assume OLS was used
debiased: bool = False¶: Flag indicating to apply a small sample adjustment
constraints: LinearConstraint | None = None¶: Constraints used in estimation, if any

Notes

If GLS is used, the covariance is estimated by

\[(X'\Omega^{-1}X)^{-1}\]

where X is a block diagonal matrix of exogenous variables. When GLS is not used, the covariance is estimated by

\[(X'X)^{-1}(X'\Omega X)(X'X)^{-1}\]

Methods

Properties

`cov`	Parameter covariance
`cov_config`	Optional configuration information used in covariance
`sigma`	Error covariance