def test_kernel_weight_direct(weight_data, center, debias):
bandwidth = 12
wm = KernelWeightMatrix(center,
debias,
kernel="parzen",
bandwidth=bandwidth)
x, z, eps, sigma = weight_data
weights = wm.weight_matrix(x, z, eps, sigma=sigma)
k = len(z)
ze = [z[i] * eps[:, i:i + 1] for i in range(k)]
ze = np.concatenate(ze, 1)
if center:
ze = ze - ze.mean(0)
nobs = ze.shape[0]
direct = ze.T @ ze / nobs
w = kernel_weight_parzen(bandwidth)
for i in range(1, bandwidth + 1):
op = ze[:-i].T @ ze[i:] / nobs
direct += w[i] * (op + op.T)
if debias:
df = [vx.shape[1] * np.ones(vz.shape[1]) for vx, vz in zip(x, z)]
df = np.concatenate(df)[:, None]
df = np.sqrt(df)
adj = nobs / (nobs - df @ df.T)
direct *= adj
assert_allclose(weights, direct)
def test_gmm_kernel_direct(cov_data):
x, z, eps, sigma = cov_data
bandwidth = 12
k = len(x)
nobs = x[0].shape[0]
wm = KernelWeightMatrix(kernel='bartlett', bandwidth=bandwidth)
w = wm.weight_matrix(x, z, eps, sigma=sigma)
cov_est = GMMKernelCovariance(x, z, eps, w, sigma=sigma, debiased=debias, kernel='bartlett',
bandwidth=bandwidth)
xpz_wi_zpxi = _xpz_wi_zpxi(x, z, w)
xpz = _xpz(x, z)
wi = np.linalg.inv(w)
xpz_wi = xpz @ wi
ze = [z[i] * eps[:, i:i + 1] for i in range(k)]
ze = np.concatenate(ze, 1)
zeez = ze.T @ ze / nobs
w = kernel_weight_bartlett(bandwidth)
for i in range(1, bandwidth + 1):
op = ze[:-i].T @ ze[i:] / nobs
zeez += w[i] * (op + op.T)
assert_allclose(zeez, cov_est._omega())
direct = xpz_wi_zpxi @ (xpz_wi @ zeez @ xpz_wi.T) @ xpz_wi_zpxi / nobs
direct = (direct + direct.T) / 2
if debias:
df = [vx.shape[1] * np.ones(vx.shape[1]) for vx in x]
df = np.concatenate(df)[:, None]
df = np.sqrt(df)
adj = nobs / (nobs - df @ df.T)
direct *= adj
direct = (direct + direct.T) / 2
assert_allclose(direct, cov_est.cov)