def test_singular():
"""Runs the high-dimensional case.
"""
p = 2
n = 13
sigma = np.eye(p, p)
data = np.random.multivariate_normal(np.zeros(p), sigma, n)
data = np.hstack((data, data))
with pytest.raises(ValueError):
sigma_tilde = nls.shrink_cov(data, 0)
def test_large_p():
"""Runs the high-dimensional case.
"""
p = 13
n = 12
sigma = np.eye(p, p)
data = np.random.multivariate_normal(np.zeros(p), sigma, n)
sigma_tilde = nls.shrink_cov(data, 0)
S = np.sum(sigma_tilde[np.eye(p) == 0]) / n_choose_k(p, 2) / np.sum(np.diag(sigma_tilde)) * p
assert S < 1 # assert that the diagonal is the major contributor
def test_ols():
"""Runs the high-dimensional case.
"""
p = 2
n = 14
sigma = np.eye(p, p)
data = np.random.multivariate_normal(np.zeros(p), sigma, n) + np.arange(n)[:, np.newaxis] + 1
x = np.vstack((np.ones(n).T, np.arange(n).T)).T
betahat = np.linalg.solve(np.dot(x.T, x), np.dot(x.T, data))
datahat = np.dot(x, betahat)
res = data - datahat
sigma_tilde = nls.shrink_cov(res, k=2) # corresponding to 2 degrees of freedom
S = np.sum(sigma_tilde[np.eye(p) == 0]) / n_choose_k(p, 2) / np.sum(np.diag(sigma_tilde)) * p
assert S < 1 # assert that the diagonal is the major contributor
def test_analytic_shrinkage():
"""Runs the most simple possible test: 2 variables with 12 samples.
"""
x = np.array([[-0.98511153, -0.2599713],
[0.20374114, -0.59699234],
[0.28570754, 0.77542166],
[-0.78768299, 0.45808448],
[0.80494623, -2.16308943],
[-2.01761751, -0.27944538],
[-0.24710646, -0.33260174],
[0.369508, 0.57123535],
[2.07913481, -0.0749686],
[1.07194672, -0.69343179],
[-0.11947645, -1.45457297],
[-0.54877366, -1.21191041]])
expected = np.array([[1.04344299, 0.0335051],
[0.0335051, 1.11112703]])
sigma_tilde = nls.shrink_cov(x, 0)
np.testing.assert_allclose(sigma_tilde, expected)
ps = np.arange(start=10, stop=200, step=20)
print(ps)
e_prial = np.zeros(len(ps))
for i, p in enumerate(ps):
reps = int(np.maximum(100, np.minimum(100, 1e5 / p)))
prial = np.zeros(reps, dtype=float)
for j in np.arange(reps):
n = 600
lam = np.concatenate([np.ones(int(p / 5)),
3 * np.ones(int(2 * p / 5.)),
10 * np.ones(int(2 * p / 5.))])
sigma = np.diag(np.ones(p) * lam)
xx = np.random.randn(n, p)
d, u = np.linalg.eigh(sigma)
# y = np.linalg.solve(u.T, xx.T)
s_sqrt = np.eye(p, p) * np.sqrt(lam)
y = np.dot(xx, s_sqrt)
s_tilde = nls.shrink_cov(y)
s_sample = np.cov(y.T)
pr = ana.prial(s_sample, s_tilde, sigma)
prial[j] = float(pr)
e_prial[i] = np.mean(prial)
print(np.mean(prial))
print(e_prial)
def nonlin_shrink(self):
S_nlshrink = nls.shrink_cov(self.X)
return S_nlshrink