def cov(self) -> NDArray:
"""Parameter covariance"""
x, z = self._x, self._z
k = len(x)
nobs = x[0].shape[0]
xpz = blocked_cross_prod(x, z, eye(k))
xpz /= nobs
wi = inv(self._w)
xpz_wi_zpx = xpz @ wi @ xpz.T
omega = self._omega()
xpz_wi_omega_wi_zpx = xpz @ wi @ omega @ wi @ xpz.T
adj = self._adjustment()
if self._constraints is None:
xpz_wi_zpxi = inv(xpz_wi_zpx)
cov = xpz_wi_zpxi @ xpz_wi_omega_wi_zpx @ xpz_wi_zpxi / nobs
else:
cons = self._constraints
xpz_wi_zpx = cons.t.T @ xpz_wi_zpx @ cons.t
xpz_wi_zpxi = inv(xpz_wi_zpx)
xpz_wi_omega_wi_zpx = cons.t.T @ xpz_wi_omega_wi_zpx @ cons.t
cov = (cons.t @ xpz_wi_zpxi @ xpz_wi_omega_wi_zpx @ xpz_wi_zpxi
@ cons.t.T / nobs)
cov = (cov + cov.T) / 2
return adj * cov
def test_blocked_outer_product():
nobs = 200
k = 3
x = [np.random.standard_normal((nobs, k)) for _ in range(k)]
z = [np.random.standard_normal((nobs, k + 2)) for _ in range(k)]
scale = np.linspace(1, 2, k)
s = np.ones(k) * (scale[:, None] @ scale[None, :]) + np.diag(np.arange(1, k + 1))
actual = blocked_cross_prod(x, z, s)
_x = []
_z = []
for i in range(k):
xrow = []
zrow = []
for j in range(k):
if i == j:
xrow.append(x[i])
zrow.append(z[i])
else:
xrow.append(np.zeros((nobs, k)))
zrow.append(np.zeros((nobs, k + 2)))
_x.append(np.concatenate(xrow, 1))
_z.append(np.concatenate(zrow, 1))
_x = np.concatenate(_x, 0)
_z = np.concatenate(_z, 0)
desired = _x.T @ np.kron(s, np.eye(nobs)) @ _z
assert_allclose(actual, desired)