def _estimate_kappa(self):
y, x, z = self._wy, self._wx, self._wz
is_exog = self._regressor_is_exog
e = c_[y, x[:, ~is_exog]]
x1 = x[:, is_exog]
ez = e - z @ (pinv(z) @ e)
ex1 = e - x1 @ (pinv(x1) @ e)
vpmzv_sqinv = inv_sqrth(ez.T @ ez)
q = vpmzv_sqinv @ (ex1.T @ ex1) @ vpmzv_sqinv
return min(eigvalsh(q))
def _estimate_kappa(self) -> float:
y, x, z = self._wy, self._wx, self._wz
is_exog = self._regressor_is_exog
e = c_[y, x[:, ~is_exog]]
x1 = x[:, is_exog]
ez = e - z @ (pinv(z) @ e)
if x1.shape[1] == 0: # No exogenous regressors
ex1 = e
else:
ex1 = e - x1 @ (pinv(x1) @ e)
vpmzv_sqinv = inv_sqrth(ez.T @ ez)
q = vpmzv_sqinv @ (ex1.T @ ex1) @ vpmzv_sqinv
return min(eigvalsh(q))
def test_inv_sqrth():
x = np.random.randn(1000, 10)
xpx = x.T @ x
invsq = inv_sqrth(xpx)
prod = invsq @ xpx @ invsq - np.eye(10)
assert_allclose(1 + prod, np.ones((10, 10)))