def quadratic_form_test(
params: ArrayLike,
cov: ArrayLike,
restriction: OptionalArrayLike = None,
value: OptionalArrayLike = None,
formula: Optional[Union[str, List[str]]] = None,
) -> WaldTestStatistic:
if formula is not None and restriction is not None:
raise ValueError("restriction and formula cannot be used"
"simultaneously.")
if formula is not None:
assert isinstance(params, Series)
di = DesignInfo(list(params.index))
lc = di.linear_constraint(formula)
restriction, value = lc.coefs, lc.constants
restriction = np.asarray(restriction)
if value is None:
value = np.zeros(restriction.shape[0])
value = np.asarray(value).ravel()[:, None]
diff = restriction @ np.asarray(params)[:, None] - value
rcov = restriction @ cov @ restriction.T
stat = float(diff.T @ np.linalg.inv(rcov) @ diff)
df = restriction.shape[0]
null = "Linear equality constraint is valid"
name = "Linear Equality Hypothesis Test"
return WaldTestStatistic(stat, null, df, name=name)
def quadratic_form_test(params, cov, restriction=None, value=None, formula=None):
if formula is not None and restriction is not None:
raise ValueError('restriction and formula cannot be used'
'simultaneously.')
if formula is not None:
di = DesignInfo(list(params.index))
lc = di.linear_constraint(formula)
restriction, value = lc.coefs, lc.constants
restriction = np.asarray(restriction)
if value is None:
value = np.zeros(restriction.shape[0])
value = np.asarray(value).ravel()[:, None]
diff = restriction @ params.values[:, None] - value
rcov = restriction @ cov @ restriction.T
stat = float(diff.T @ np.linalg.inv(rcov) @ diff)
df = restriction.shape[0]
null = 'Linear equality constraint is valid'
name = 'Linear Equality Hypothesis Test'
return WaldTestStatistic(stat, null, df, name=name)