def test_debiased(self, kernel, data, bandwidth):
wm = KernelWeightMatrix(debiased=True, kernel=kernel.kernel, bandwidth=bandwidth)
weight = wm.weight_matrix(data.x, data.z, data.e)
z, e, nobs, nvar = data.z, data.e, data.nobs, data.nvar
bw = bandwidth or nobs - 2
w = kernel.weight(bw, nobs - 1)
ze = z * e
s = ze.T @ ze
for i in range(1, len(w)):
op = ze[i:].T @ ze[:-i]
s += w[i] * (op + op.T)
assert_allclose(weight, s / (nobs - nvar))
assert wm.config['bandwidth'] == bw
assert wm.config['kernel'] == kernel.kernel
def test_kernel(self, data, kernel, bandwidth):
c = IVGMMCovariance(
data.x,
data.y,
data.z,
data.params,
data.i,
"kernel",
kernel=kernel.kernel,
bandwidth=bandwidth,
)
s = KernelWeightMatrix(kernel=kernel.kernel,
bandwidth=bandwidth).weight_matrix(
data.x, data.z, data.e)
x, z, nobs = data.x, data.z, data.nobs
xzwswzx = x.T @ z @ s @ z.T @ x / data.nobs
cov = data.xzizx_inv @ xzwswzx @ data.xzizx_inv
cov = (cov + cov.T) / 2
assert_allclose(c.cov, cov)
assert c.config["kernel"] == kernel.kernel
assert c.config["debiased"] is False
assert c.config["bandwidth"] == bandwidth or nobs - 2
c = IVGMMCovariance(data.x, data.y, data.z, data.params, data.i,
"kernel")
assert "Kernel" in str(c)
def test_center(self, data, kernel, bandwidth):
wm = KernelWeightMatrix(kernel.kernel,
bandwidth,
center=True,
optimal_bw=True)
weight = wm.weight_matrix(data.x, data.z, data.e)
z, e, nobs = data.z, data.e, data.nobs
bw = bandwidth or wm.bandwidth
w = kernel.weight(bw, nobs - 1)
ze = z * e
ze = ze - ze.mean(0)
s = ze.T @ ze
for i in range(1, len(w)):
op = ze[i:].T @ ze[:-i]
s += w[i] * (op + op.T)
assert_allclose(weight, s / nobs)
assert wm.config['bandwidth'] == bw
assert wm.config['kernel'] == kernel.kernel
for name in kernel.alt_names:
wm = KernelWeightMatrix(name,
bandwidth,
center=True,
optimal_bw=True)
weight2 = wm.weight_matrix(data.x, data.z, data.e)
assert_equal(weight, weight2)
def test_config(self, data, kernel, bandwidth):
wm = KernelWeightMatrix(kernel=kernel.kernel, bandwidth=bandwidth)
weight = wm.weight_matrix(data.x, data.z, data.e)
z, e, nobs = data.z, data.e, data.nobs
bw = bandwidth or wm.bandwidth
w = kernel.weight(bw, nobs - 1)
ze = z * e
s = ze.T @ ze
for i in range(1, len(w)):
op = ze[i:].T @ ze[:-i]
s += w[i] * (op + op.T)
assert_allclose(weight, s / nobs)
assert wm.config['center'] is False
assert wm.config['debiased'] is False
assert wm.config['bandwidth'] == bw
assert wm.config['kernel'] == kernel.kernel
for name in kernel.alt_names:
wm = KernelWeightMatrix(kernel=name, bandwidth=bandwidth)
weight2 = wm.weight_matrix(data.x, data.z, data.e)
assert_equal(weight, weight2)