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_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_conf_int_bias_corrected(self):
num_bootstrap = 20
bs = IIDBootstrap(self.x)
bs.seed(23456)
def func(y):
return y.mean(axis=0)
ci = bs.conf_int(func, reps=num_bootstrap, method='bc')
bs.reset()
ci_db = bs.conf_int(func, reps=num_bootstrap, method='debiased')
assert_equal(ci, ci_db)
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)
q = stats.norm.ppf(np.array([0.025, 0.975]))
q = q[:, None]
percentiles = 100 * stats.norm.cdf(2 * 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_db, ci)
def test_conf_int_bias_corrected(self):
num_bootstrap = 20
bs = IIDBootstrap(self.x)
bs.seed(23456)
def func(y):
return y.mean(axis=0)
ci = bs.conf_int(func, reps=num_bootstrap, method='bc')
bs.reset()
ci_db = bs.conf_int(func, reps=num_bootstrap, method='debiased')
assert_equal(ci, ci_db)
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)
q = stats.norm.ppf(np.array([0.025, 0.975]))
q = q[:, None]
percentiles = 100 * stats.norm.cdf(2 * 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_db, ci)
def test_reset(self):
bs = IIDBootstrap(np.arange(100))
state = bs.get_state()
for data, kwdata in bs.bootstrap(10):
final = data[0]
bs.reset()
state_reset = bs.get_state()
for data, kwdata in bs.bootstrap(10):
final_reset = data[0]
assert_equal(final, final_reset)
assert_equal(state, state_reset)
def test_apply(self):
bs = IIDBootstrap(self.x)
bs.seed(23456)
results = bs.apply(self.func, 1000)
bs.reset(23456)
direct_results = []
for pos, _ in bs.bootstrap(1000):
direct_results.append(self.func(*pos))
direct_results = np.array(direct_results)
assert_equal(results, direct_results)
def test_reset(self):
bs = IIDBootstrap(np.arange(100))
state = bs.get_state()
for data, _ in bs.bootstrap(10):
final = data[0]
bs.reset()
state_reset = bs.get_state()
for data, _ in bs.bootstrap(10):
final_reset = data[0]
assert_equal(final, final_reset)
assert_equal(state, state_reset)
def test_apply(bs_setup):
bs = IIDBootstrap(bs_setup.x)
bs.seed(23456)
results = bs.apply(bs_setup.func, 1000)
bs.reset(True)
direct_results = []
for pos, _ in bs.bootstrap(1000):
direct_results.append(bs_setup.func(*pos))
direct_results = np.array(direct_results)
assert_equal(results, direct_results)
def test_apply_series(self):
bs = IIDBootstrap(self.y_series)
bs.seed(23456)
results = bs.apply(self.func, 1000)
bs.reset(23456)
direct_results = []
for pos, _ in bs.bootstrap(1000):
direct_results.append(self.func(*pos))
direct_results = np.array(direct_results)
direct_results = direct_results[:, None]
assert_equal(results, direct_results)
def test_apply(self):
bs = IIDBootstrap(self.x)
bs.seed(23456)
def func(y):
return y.mean(0)
results = bs.apply(func, 1000)
bs.reset(23456)
direct_results = []
for pos, kw in bs.bootstrap(1000):
direct_results.append(func(*pos))
direct_results = np.array(direct_results)
assert_equal(results, direct_results)
def test_apply_series(self):
bs = IIDBootstrap(self.y_series)
bs.seed(23456)
def func(y):
return y.mean(0)
results = bs.apply(func, 1000)
bs.reset(23456)
direct_results = []
for pos, kw in bs.bootstrap(1000):
direct_results.append(func(*pos))
direct_results = np.array(direct_results)
direct_results = direct_results[:, None]
assert_equal(results, direct_results)
def test_cov(self):
bs = IIDBootstrap(self.x)
num_bootstrap = 10
cov = bs.cov(func=self.func, reps=num_bootstrap, recenter=False)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for data, _ in bs.bootstrap(num_bootstrap):
results[count] = data[0].mean(axis=0)
count += 1
errors = results - self.x.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs.reset()
cov = bs.cov(func=self.func, recenter=True, reps=num_bootstrap)
errors = results - results.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs = IIDBootstrap(self.x_df)
cov = bs.cov(func=self.func, reps=num_bootstrap, recenter=False)
bs.reset()
var = bs.var(func=self.func, reps=num_bootstrap, recenter=False)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for data, _ in bs.bootstrap(num_bootstrap):
results[count] = data[0].mean(axis=0)
count += 1
errors = results - self.x.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
assert_allclose(var, np.diag(direct_cov))
bs.reset()
cov = bs.cov(func=self.func, recenter=True, reps=num_bootstrap)
errors = results - results.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
def test_cov(bs_setup):
bs = IIDBootstrap(bs_setup.x)
num_bootstrap = 10
cov = bs.cov(func=bs_setup.func, reps=num_bootstrap, recenter=False)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for data, _ in bs.bootstrap(num_bootstrap):
results[count] = data[0].mean(axis=0)
count += 1
errors = results - bs_setup.x.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs.reset()
cov = bs.cov(func=bs_setup.func, recenter=True, reps=num_bootstrap)
errors = results - results.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs = IIDBootstrap(bs_setup.x_df)
cov = bs.cov(func=bs_setup.func, reps=num_bootstrap, recenter=False)
bs.reset()
var = bs.var(func=bs_setup.func, reps=num_bootstrap, recenter=False)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for data, _ in bs.bootstrap(num_bootstrap):
results[count] = data[0].mean(axis=0)
count += 1
errors = results - bs_setup.x.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
assert_allclose(var, np.diag(direct_cov))
bs.reset()
cov = bs.cov(func=bs_setup.func, recenter=True, reps=num_bootstrap)
errors = results - results.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
def test_conf_int_percentile(self):
num_bootstrap = 200
bs = IIDBootstrap(self.x)
def func(y):
return y.mean(axis=0)
ci = bs.conf_int(func, reps=num_bootstrap, size=0.90,
method='percentile')
bs.reset()
ci_u = bs.conf_int(func, tail='upper', reps=num_bootstrap, size=0.95,
method='percentile')
bs.reset()
ci_l = bs.conf_int(func, tail='lower', reps=num_bootstrap, size=0.95,
method='percentile')
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for pos, kw in bs.bootstrap(num_bootstrap):
results[count] = func(*pos)
count += 1
upper = np.percentile(results, 95, axis=0)
lower = np.percentile(results, 5, axis=0)
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_norm(bs_setup):
num_bootstrap = 200
bs = IIDBootstrap(bs_setup.x)
ci = bs.conf_int(bs_setup.func, reps=num_bootstrap, size=0.90, method="norm")
bs.reset()
ci_u = bs.conf_int(
bs_setup.func, tail="upper", reps=num_bootstrap, size=0.95, method="var"
)
bs.reset()
ci_l = bs.conf_int(
bs_setup.func, tail="lower", reps=num_bootstrap, size=0.95, method="cov"
)
bs.reset()
cov = bs.cov(bs_setup.func, reps=num_bootstrap)
mu = bs_setup.func(bs_setup.x)
std_err = np.sqrt(np.diag(cov))
upper = mu + stats.norm.ppf(0.95) * std_err
lower = mu + stats.norm.ppf(0.05) * std_err
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_percentile(bs_setup):
num_bootstrap = 200
bs = IIDBootstrap(bs_setup.x)
ci = bs.conf_int(bs_setup.func, reps=num_bootstrap, size=0.90, method="percentile")
bs.reset()
ci_u = bs.conf_int(
bs_setup.func, tail="upper", reps=num_bootstrap, size=0.95, method="percentile"
)
bs.reset()
ci_l = bs.conf_int(
bs_setup.func, tail="lower", reps=num_bootstrap, size=0.95, method="percentile"
)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for pos, _ in bs.bootstrap(num_bootstrap):
results[count] = bs_setup.func(*pos)
count += 1
upper = np.percentile(results, 95, axis=0)
lower = np.percentile(results, 5, axis=0)
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_norm(self):
num_bootstrap = 200
bs = IIDBootstrap(self.x)
ci = bs.conf_int(self.func,
reps=num_bootstrap,
size=0.90,
method='norm')
bs.reset()
ci_u = bs.conf_int(self.func,
tail='upper',
reps=num_bootstrap,
size=0.95,
method='var')
bs.reset()
ci_l = bs.conf_int(self.func,
tail='lower',
reps=num_bootstrap,
size=0.95,
method='cov')
bs.reset()
cov = bs.cov(self.func, reps=num_bootstrap)
mu = self.func(self.x)
std_err = np.sqrt(np.diag(cov))
upper = mu + stats.norm.ppf(0.95) * std_err
lower = mu + stats.norm.ppf(0.05) * std_err
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_percentile(self):
num_bootstrap = 200
bs = IIDBootstrap(self.x)
def func(y):
return y.mean(axis=0)
ci = bs.conf_int(func, reps=num_bootstrap, size=0.90,
method='percentile')
bs.reset()
ci_u = bs.conf_int(func, tail='upper', reps=num_bootstrap, size=0.95,
method='percentile')
bs.reset()
ci_l = bs.conf_int(func, tail='lower', reps=num_bootstrap, size=0.95,
method='percentile')
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for pos, kw in bs.bootstrap(num_bootstrap):
results[count] = func(*pos)
count += 1
upper = np.percentile(results, 95, axis=0)
lower = np.percentile(results, 5, axis=0)
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_basic(self):
num_bootstrap = 200
bs = IIDBootstrap(self.x)
ci = bs.conf_int(self.func, reps=num_bootstrap, size=0.90, method='basic')
bs.reset()
ci_u = bs.conf_int(self.func, tail='upper', reps=num_bootstrap, size=0.95,
method='basic')
bs.reset()
ci_l = bs.conf_int(self.func, tail='lower', reps=num_bootstrap, size=0.95,
method='basic')
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for pos, _ in bs.bootstrap(num_bootstrap):
results[count] = self.func(*pos)
count += 1
mu = self.func(self.x)
upper = mu + (mu - np.percentile(results, 5, axis=0))
lower = mu + (mu - np.percentile(results, 95, axis=0))
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_basic(self):
num_bootstrap = 200
bs = IIDBootstrap(self.x)
ci = bs.conf_int(self.func, reps=num_bootstrap, size=0.90, method='basic')
bs.reset()
ci_u = bs.conf_int(self.func, tail='upper', reps=num_bootstrap, size=0.95,
method='basic')
bs.reset()
ci_l = bs.conf_int(self.func, tail='lower', reps=num_bootstrap, size=0.95,
method='basic')
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for pos, _ in bs.bootstrap(num_bootstrap):
results[count] = self.func(*pos)
count += 1
mu = self.func(self.x)
upper = mu + (mu - np.percentile(results, 5, axis=0))
lower = mu + (mu - np.percentile(results, 95, axis=0))
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_conf_int_norm(self):
num_bootstrap = 200
bs = IIDBootstrap(self.x)
def func(y):
return y.mean(axis=0)
ci = bs.conf_int(func, reps=num_bootstrap, size=0.90,
method='norm')
bs.reset()
ci_u = bs.conf_int(func, tail='upper', reps=num_bootstrap, size=0.95,
method='var')
bs.reset()
ci_l = bs.conf_int(func, tail='lower', reps=num_bootstrap, size=0.95,
method='cov')
bs.reset()
cov = bs.cov(func, reps=num_bootstrap)
mu = func(self.x)
std_err = np.sqrt(np.diag(cov))
upper = mu + stats.norm.ppf(0.95) * std_err
lower = mu + stats.norm.ppf(0.05) * std_err
assert_allclose(lower, ci[0, :])
assert_allclose(upper, ci[1, :])
assert_allclose(ci[1, :], ci_u[1, :])
assert_allclose(ci[0, :], ci_l[0, :])
inf = np.empty_like(ci_l[0, :])
inf.fill(np.inf)
assert_equal(inf, ci_l[1, :])
assert_equal(-1 * inf, ci_u[0, :])
def test_cov(self):
def func(y):
return y.mean(axis=0)
bs = IIDBootstrap(self.x)
num_bootstrap = 10
cov = bs.cov(func=func, reps=num_bootstrap, recenter=False)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for data, kw in bs.bootstrap(num_bootstrap):
results[count] = data[0].mean(axis=0)
count += 1
errors = results - self.x.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs.reset()
cov = bs.cov(func=func, recenter=True, reps=num_bootstrap)
errors = results - results.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs = IIDBootstrap(self.x_df)
cov = bs.cov(func=func, reps=num_bootstrap, recenter=False)
bs.reset()
results = np.zeros((num_bootstrap, 2))
count = 0
for data, kw in bs.bootstrap(num_bootstrap):
results[count] = data[0].mean(axis=0)
count += 1
errors = results - self.x.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
bs.reset()
cov = bs.cov(func=func, recenter=True, reps=num_bootstrap)
errors = results - results.mean(axis=0)
direct_cov = errors.T.dot(errors) / num_bootstrap
assert_allclose(cov, direct_cov)
def test_conf_int_parametric(self):
def param_func(x, params=None, state=None):
if state is not None:
mu = params
e = state.standard_normal(x.shape)
return (mu + e).mean(0)
else:
return x.mean(0)
def semi_func(x, params=None):
if params is not None:
mu = params
e = x - mu
return (mu + e).mean(0)
else:
return x.mean(0)
reps = 100
bs = IIDBootstrap(self.x)
bs.seed(23456)
ci = bs.conf_int(func=param_func, reps=reps, sampling='parametric')
assert len(ci) == 2
assert np.all(ci[0] < ci[1])
bs.reset()
results = np.zeros((reps, 2))
count = 0
mu = self.x.mean(0)
for pos, _ in bs.bootstrap(100):
results[count] = param_func(*pos, params=mu,
state=bs.random_state)
count += 1
assert_equal(bs._results, results)
bs.reset()
ci = bs.conf_int(func=semi_func, reps=100, sampling='semi')
assert len(ci) == 2
assert np.all(ci[0] < ci[1])
bs.reset()
results = np.zeros((reps, 2))
count = 0
for pos, _ in bs.bootstrap(100):
results[count] = semi_func(*pos, params=mu)
count += 1
assert_allclose(bs._results, results)
def test_conf_int_parametric(self):
def param_func(x, params=None, state=None):
if state is not None:
mu = params
e = state.standard_normal(x.shape)
return (mu + e).mean(0)
else:
return x.mean(0)
def semi_func(x, params=None):
if params is not None:
mu = params
e = x - mu
return (mu + e).mean(0)
else:
return x.mean(0)
reps = 100
bs = IIDBootstrap(self.x)
bs.seed(23456)
ci = bs.conf_int(func=param_func, reps=reps, sampling='parametric')
assert len(ci) == 2
assert np.all(ci[0] < ci[1])
bs.reset()
results = np.zeros((reps, 2))
count = 0
mu = self.x.mean(0)
for pos, _ in bs.bootstrap(100):
results[count] = param_func(*pos, params=mu,
state=bs.random_state)
count += 1
assert_equal(bs._results, results)
bs.reset()
ci = bs.conf_int(func=semi_func, reps=100, sampling='semi')
assert len(ci) == 2
assert np.all(ci[0] < ci[1])
bs.reset()
results = np.zeros((reps, 2))
count = 0
for pos, _ in bs.bootstrap(100):
results[count] = semi_func(*pos, params=mu)
count += 1
assert_allclose(bs._results, results)
def test_studentized(bs_setup):
num_bootstrap = 20
bs = IIDBootstrap(bs_setup.x)
bs.seed(23456)
def std_err_func(mu, y):
errors = y - mu
var = (errors ** 2.0).mean(axis=0)
return np.sqrt(var / y.shape[0])
ci = bs.conf_int(
bs_setup.func,
reps=num_bootstrap,
method="studentized",
std_err_func=std_err_func,
)
bs.reset()
base = bs_setup.func(bs_setup.x)
results = np.zeros((num_bootstrap, 2))
stud_results = np.zeros((num_bootstrap, 2))
count = 0
for pos, _ in bs.bootstrap(reps=num_bootstrap):
results[count] = bs_setup.func(*pos)
std_err = std_err_func(results[count], *pos)
stud_results[count] = (results[count] - base) / std_err
count += 1
assert_allclose(results, bs._results)
assert_allclose(stud_results, bs._studentized_results)
errors = results - results.mean(0)
std_err = np.sqrt(np.mean(errors ** 2.0, axis=0))
ci_direct = np.zeros((2, 2))
for i in range(2):
ci_direct[0, i] = base[i] - std_err[i] * np.percentile(stud_results[:, i], 97.5)
ci_direct[1, i] = base[i] - std_err[i] * np.percentile(stud_results[:, i], 2.5)
assert_allclose(ci, ci_direct)
bs.reset()
ci = bs.conf_int(
bs_setup.func, reps=num_bootstrap, method="studentized", studentize_reps=50
)
bs.reset()
base = bs_setup.func(bs_setup.x)
results = np.zeros((num_bootstrap, 2))
stud_results = np.zeros((num_bootstrap, 2))
count = 0
for pos, _ in bs.bootstrap(reps=num_bootstrap):
results[count] = bs_setup.func(*pos)
inner_bs = IIDBootstrap(*pos)
seed = bs.random_state.randint(2 ** 31 - 1)
inner_bs.seed(seed)
cov = inner_bs.cov(bs_setup.func, reps=50)
std_err = np.sqrt(np.diag(cov))
stud_results[count] = (results[count] - base) / std_err
count += 1
assert_allclose(results, bs._results)
assert_allclose(stud_results, bs._studentized_results)
errors = results - results.mean(0)
std_err = np.sqrt(np.mean(errors ** 2.0, axis=0))
ci_direct = np.zeros((2, 2))
for i in range(2):
ci_direct[0, i] = base[i] - std_err[i] * np.percentile(stud_results[:, i], 97.5)
ci_direct[1, i] = base[i] - std_err[i] * np.percentile(stud_results[:, i], 2.5)
assert_allclose(ci, ci_direct)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
bs.conf_int(
bs_setup.func,
reps=num_bootstrap,
method="studentized",
std_err_func=std_err_func,
reuse=True,
)
assert_equal(len(w), 1)
def test_studentized(self):
num_bootstrap = 20
bs = IIDBootstrap(self.x)
bs.seed(23456)
def func(y):
return y.mean(axis=0)
def std_err_func(mu, y):
errors = y - mu
var = (errors ** 2.0).mean(axis=0)
return np.sqrt(var / y.shape[0])
ci = bs.conf_int(func, reps=num_bootstrap, method='studentized',
std_err_func=std_err_func)
bs.reset()
base = func(self.x)
results = np.zeros((num_bootstrap, 2))
stud_results = np.zeros((num_bootstrap, 2))
count = 0
for pos, kwdata in bs.bootstrap(reps=num_bootstrap):
results[count] = func(*pos)
std_err = std_err_func(results[count], *pos)
stud_results[count] = (results[count] - base) / std_err
count += 1
assert_allclose(results, bs._results)
assert_allclose(stud_results, bs._studentized_results)
errors = results - results.mean(0)
std_err = np.sqrt(np.mean(errors ** 2.0, axis=0))
ci_direct = np.zeros((2, 2))
for i in range(2):
ci_direct[0, i] = base[i] - std_err[i] * np.percentile(
stud_results[:, i], 97.5)
ci_direct[1, i] = base[i] - std_err[i] * np.percentile(
stud_results[:, i], 2.5)
assert_allclose(ci, ci_direct)
bs.reset()
ci = bs.conf_int(func, reps=num_bootstrap, method='studentized',
studentize_reps=50)
bs.reset()
base = func(self.x)
results = np.zeros((num_bootstrap, 2))
stud_results = np.zeros((num_bootstrap, 2))
count = 0
for pos, kwdata in bs.bootstrap(reps=num_bootstrap):
results[count] = func(*pos)
inner_bs = IIDBootstrap(*pos)
seed = bs.random_state.randint(2 ** 31 - 1)
inner_bs.seed(seed)
cov = inner_bs.cov(func, reps=50)
std_err = np.sqrt(np.diag(cov))
stud_results[count] = (results[count] - base) / std_err
count += 1
assert_allclose(results, bs._results)
assert_allclose(stud_results, bs._studentized_results)
errors = results - results.mean(0)
std_err = np.sqrt(np.mean(errors ** 2.0, axis=0))
ci_direct = np.zeros((2, 2))
for i in range(2):
ci_direct[0, i] = base[i] - std_err[i] * np.percentile(
stud_results[:, i], 97.5)
ci_direct[1, i] = base[i] - std_err[i] * np.percentile(
stud_results[:, i], 2.5)
assert_allclose(ci, ci_direct)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
bs.conf_int(func, reps=num_bootstrap, method='studentized',
std_err_func=std_err_func, reuse=True)
assert_equal(len(w), 1)
