def test_bca(self):
num_bootstrap = 20
bs = IIDBootstrap(self.x)
bs.seed(23456)
ci_direct = bs.conf_int(self.func, reps=num_bootstrap, method='bca')
bs.reset()
base, results = bs._base, bs._results
p = np.zeros(2)
p[0] = np.mean(results[:, 0] < base[0])
p[1] = np.mean(results[:, 1] < base[1])
b = stats.norm.ppf(p)
b = b[:, None]
q = stats.norm.ppf(np.array([0.025, 0.975]))
base = self.func(self.x)
nobs = self.x.shape[0]
jk = _loo_jackknife(self.func, nobs, [self.x], {})
u = jk.mean() - jk
u2 = np.sum(u * u, 0)
u3 = np.sum(u * u * u, 0)
a = u3 / (6.0 * (u2**1.5))
a = a[:, None]
percentiles = 100 * stats.norm.cdf(b + (b + q) / (1 - a * (b + q)))
ci = np.zeros((2, 2))
for i in range(2):
ci[i] = np.percentile(results[:, i], list(percentiles[i]))
ci = ci.T
assert_allclose(ci_direct, ci)
def test_bca(self):
num_bootstrap = 20
bs = IIDBootstrap(self.x)
bs.seed(23456)
def func(y):
return y.mean(axis=0)
ci_direct = bs.conf_int(func, reps=num_bootstrap, method='bca')
bs.reset()
base, results = bs._base, bs._results
p = np.zeros(2)
p[0] = np.mean(results[:, 0] < base[0])
p[1] = np.mean(results[:, 1] < base[1])
b = stats.norm.ppf(p)
b = b[:, None]
q = stats.norm.ppf(np.array([0.025, 0.975]))
base = func(self.x)
nobs = self.x.shape[0]
jk = _loo_jackknife(func, nobs, [self.x], {})
u = (nobs - 1) * (jk - base)
u2 = np.sum(u * u, 0)
u3 = np.sum(u * u * u, 0)
a = u3 / (6.0 * (u2 ** 1.5))
a = a[:, None]
percentiles = 100 * stats.norm.cdf(b + (b + q) / (1 - a * (b + q)))
ci = np.zeros((2, 2))
for i in range(2):
ci[i] = np.percentile(results[:, i], list(percentiles[i]))
ci = ci.T
assert_allclose(ci_direct, ci)
def test_jackknife(self):
def func(x):
return x.mean(axis=0)
x = self.x
results = _loo_jackknife(func, len(x), (x, ), {})
direct_results = np.zeros_like(x)
for i in range(len(x)):
if i == 0:
y = x[1:]
elif i == (len(x) - 1):
y = x[:-1]
else:
temp = list(x[:i])
temp.extend(list(x[i + 1:]))
y = np.array(temp)
direct_results[i] = func(y)
assert_allclose(direct_results, results)
x = self.x_df
results_df = _loo_jackknife(func, len(x), (x, ), {})
assert_equal(results, results_df)
y = self.y
results = _loo_jackknife(func, len(y), (y, ), {})
direct_results = np.zeros_like(y)
for i in range(len(y)):
if i == 0:
z = y[1:]
elif i == (len(y) - 1):
z = y[:-1]
else:
temp = list(y[:i])
temp.extend(list(y[i + 1:]))
z = np.array(temp)
direct_results[i] = func(z)
assert_allclose(direct_results, results)
y = self.y_series
results_series = _loo_jackknife(func, len(y), (y, ), {})
assert_allclose(results, results_series)
def test_jackknife(self):
def func(x):
return x.mean(axis=0)
x = self.x
results = _loo_jackknife(func, len(x), (x,), {})
direct_results = np.zeros_like(x)
for i in range(len(x)):
if i == 0:
y = x[1:]
elif i == (len(x) - 1):
y = x[:-1]
else:
temp = list(x[:i])
temp.extend(list(x[i + 1:]))
y = np.array(temp)
direct_results[i] = func(y)
assert_allclose(direct_results, results)
x = self.x_df
results_df = _loo_jackknife(func, len(x), (x,), {})
assert_equal(results, results_df)
y = self.y
results = _loo_jackknife(func, len(y), (y,), {})
direct_results = np.zeros_like(y)
for i in range(len(y)):
if i == 0:
z = y[1:]
elif i == (len(y) - 1):
z = y[:-1]
else:
temp = list(y[:i])
temp.extend(list(y[i + 1:]))
z = np.array(temp)
direct_results[i] = func(z)
assert_allclose(direct_results, results)
y = self.y_series
results_series = _loo_jackknife(func, len(y), (y,), {})
assert_equal(results, results_series)