def s(self) -> NDArray:
"""HAC score covariance estimate"""
x, z, eps = self.x, self.z, self.eps
nobs, nvar = x.shape
pinvz = self._pinvz
xhat = z @ (pinvz @ x)
xhat_e = xhat * eps
kernel = self.config["kernel"]
bw = self.config["bandwidth"]
if bw is None:
self._auto_bandwidth = True
from linearmodels.shared.linalg import has_constant
const, loc = has_constant(xhat)
sel = ones((xhat.shape[1], 1))
if const:
sel[loc] = 0
scores = xhat_e @ sel
bw = kernel_optimal_bandwidth(scores, kernel)
self._bandwidth = bw
w = self._kernels[kernel](bw, nobs - 1)
s = cov_kernel(xhat_e, w)
return self._scale * s
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
ze = z * eps
mu = ze.mean(axis=0) if self._center else 0
ze -= mu
if self._orig_bandwidth is None and self._optimal_bw:
g = ze / ze.std(0)[None, :]
g = g.sum(1)
self._bandwidth = kernel_optimal_bandwidth(g, self._kernel)
elif self._orig_bandwidth is None:
self._bandwidth = nobs - 2
bw = self._bandwidth
assert bw is not None
w = self._kernels[self._kernel](bw, nobs - 1)
s = cov_kernel(ze, w)
s *= 1 if not self._debiased else nobs / (nobs - nvar)
return s
def test_cov_kernel():
with pytest.raises(ValueError):
cov_kernel(np.arange(100), 1 - np.arange(101) / 101)