def sigma(self, eps: NDArray, x: Sequence[NDArray]) -> NDArray:
"""
Estimate residual covariance.
Parameters
----------
eps : ndarray
The residuals from the system of equations.
x : list[ndarray]
A list of the regressor matrices for each equation in the system.
Returns
-------
ndarray
The estimated covariance matrix of the residuals.
"""
nobs = eps.shape[0]
eps = eps - eps.mean(0)
sigma = eps.T @ eps / nobs
scale = 1.0
if self._debiased:
k = array(list(map(lambda a: a.shape[1], x)))[:, None]
k = sqrt(k)
scale = nobs / (nobs - k @ k.T)
sigma *= scale
return sigma
def w(self, moments: NDArray) -> NDArray:
"""
Score/moment condition weighting matrix
Parameters
----------
moments : ndarray
Moment conditions (nobs by nmoments)
Returns
-------
ndarray
Weighting matrix computed from moment conditions
"""
if self._center:
moments = moments - moments.mean(0)[None, :]
out = self._kernel_cov(moments)
return inv(out)
def w(self, moments: NDArray) -> NDArray:
"""
Score/moment condition weighting matrix
Parameters
----------
moments : ndarray
Moment conditions (nobs by nmoments)
Returns
-------
ndarray
Weighting matrix computed from moment conditions
"""
if self._center:
moments = moments - moments.mean(0)[None, :]
nobs = moments.shape[0]
out = moments.T @ moments / nobs
return inv((out + out.T) / 2.0)
def weight_matrix(self, x: NDArray, z: NDArray, eps: NDArray) -> NDArray:
"""
Parameters
----------
x : ndarray
Model regressors (exog and endog), (nobs by nvar)
z : ndarray
Model instruments (exog and instruments), (nobs by ninstr)
eps : ndarray
Model errors (nobs by 1)
Returns
-------
ndarray
Covariance of GMM moment conditions.
"""
nobs, nvar = x.shape
mu = eps.mean(0)
s2 = (eps - mu).T @ (eps - mu) / nobs
w = s2 * z.T @ z / nobs
w *= 1 if not self._debiased else nobs / (nobs - nvar)
return w