linearmodels.system.gmm.KernelWeightMatrix

class KernelWeightMatrix(center=False, debiased=False, kernel='bartlett', bandwidth=None, optimal_bw=False)[source]

Heteroskedasticity robust weight estimation

Parameters
centerbool

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

debiasedbool

Flag indicating whether to use small-sample adjustments

kernelstr

Name of kernel to use. Supported kernels include:

  • “bartlett”, “newey-west” : Bartlett’s kernel

  • “parzen”, “gallant” : Parzen’s kernel

  • “qs”, “quadratic-spectral”, “andrews” : Quadratic spectral kernel

bandwidthfloat

Bandwidth to use for the kernel. If not provided the optimal bandwidth will be estimated.

optimal_bwbool

Flag indicating whether to estimate the optimal bandwidth, when bandwidth is None. If False, nobs - 2 is used

Notes

The weight matrix estimator is

\[\begin{split}W & = \hat{\Gamma}_0 + \sum_{i=1}^{n-1} w_i (\hat{\Gamma}_i + \hat{\Gamma}_i^\prime) \\ \hat{\Gamma}_j & = n^{-1}\sum_{i=1}^{n-j} g'_ig_{i+j} \\ g_i & = (z_{1i}\epsilon_{1i},z_{2i}\epsilon_{2i},\ldots,z_{ki}\epsilon_{ki})\end{split}\]

where \(g_i\) is the vector of scores across all equations for observation i and \(w_j\) are the kernel weights which depend on the selected kernel and bandwidth. \(z_{ji}\) 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 autocorrelation between the moment conditions.

Attributes
bandwidth

Bandwidth used to estimate covariance of moment conditions

config

Weight estimator configuration

kernel

Kernel used in estimation

Methods

sigma(eps, x)

Estimate residual covariance.

weight_matrix(x, z, eps, *[, sigma])

Construct a GMM weight matrix for a model.

Properties

bandwidth

Bandwidth used to estimate covariance of moment conditions

config

Weight estimator configuration

kernel

Kernel used in estimation