linearmodels.system.gmm.HeteroskedasticWeightMatrix¶

class linearmodels.system.gmm.HeteroskedasticWeightMatrix(center: bool = False, debiased: bool = False)[source]¶

Heteroskedasticity robust weight estimation

Parameters:¶

center: bool = False¶

Flag indicating whether to center the moment conditions by subtracting the mean before computing the weight matrix.

debiased: bool = False¶

Flag indicating whether to use small-sample adjustments

Notes

The weight matrix estimator is

\[\begin{split}W & = n^{-1}\sum_{i=1}^{n}g'_ig_i \\ g_i & = (z_{1i}\epsilon_{1i},z_{2i}\epsilon_{2i},\ldots,z_{ki}\epsilon_{ki})\end{split}\]

where \(g_i\) is the vector of scores across all equations for observation i. \(z_{ji}\) is the vector of instruments for equation j and \(\epsilon_{ji}\) is the error for equation j for observation i. This form allows for heteroskedasticity and arbitrary cross-sectional dependence between the moment conditions.

Methods

sigma(eps, x)	Estimate residual covariance.
weight_matrix(x, z, eps, *[, sigma])	Construct a GMM weight matrix for a model.

Properties

config

Weight estimator configuration