def _compute_test_stat(self, u):
n = np.shape(u)[0]
XLOO = LeaveOneOut(self.exog)
uLOO = LeaveOneOut(u[:,None]).__iter__()
I = 0
S2 = 0
for i, X_not_i in enumerate(XLOO):
u_j = uLOO.next()
u_j = np.squeeze(u_j)
# See Bootstrapping procedure on p. 357 in [1]
K = gpke(self.bw, data=-X_not_i, data_predict=-self.exog[i, :],
var_type=self.var_type, tosum=False)
f_i = (u[i] * u_j * K)
assert u_j.shape == K.shape
I += f_i.sum() # See eq. 12.7 on p. 355 in [1]
S2 += (f_i**2).sum() # See Theorem 12.1 on p.356 in [1]
assert np.size(I) == 1
assert np.size(S2) == 1
I *= 1. / (n * (n - 1))
ix_cont = _get_type_pos(self.var_type)[0]
hp = self.bw[ix_cont].prod()
S2 *= 2 * hp / (n * (n - 1))
T = n * I * np.sqrt(hp / S2)
return T
def cv_loo(self, params):
# See p. 254 in Textbook
params = np.asarray(params)
b = params[0 : self.K]
bw = params[self.K:]
LOO_X = LeaveOneOut(self.exog)
LOO_Y = LeaveOneOut(self.endog).__iter__()
L = 0
for i, X_not_i in enumerate(LOO_X):
Y = LOO_Y.next()
#print b.shape, np.dot(self.exog[i:i+1, :], b).shape, bw,
G = self.func(bw, endog=Y, exog=-np.dot(X_not_i, b)[:,None],
#data_predict=-b*self.exog[i, :])[0]
data_predict=-np.dot(self.exog[i:i+1, :], b))[0]
#print G.shape
L += (self.endog[i] - G) ** 2
# Note: There might be a way to vectorize this. See p.72 in [1]
return L / self.nobs
def cv_loo(self, params):
"""
Similar to the cross validation leave-one-out estimator.
Modified to reflect the linear components.
Parameters
----------
params : array_like
Vector consisting of the coefficients (b) and the bandwidths (bw).
The first ``k_linear`` elements are the coefficients.
Returns
-------
L : float
The value of the objective function
References
----------
See p.254 in [1]
"""
params = np.asarray(params)
b = params[0:self.k_linear]
bw = params[self.k_linear:]
LOO_X = LeaveOneOut(self.exog)
LOO_Y = LeaveOneOut(self.endog).__iter__()
LOO_Z = LeaveOneOut(self.exog_nonparametric).__iter__()
Xb = np.dot(self.exog, b)[:, None]
L = 0
for ii, X_not_i in enumerate(LOO_X):
Y = next(LOO_Y)
Z = next(LOO_Z)
Xb_j = np.dot(X_not_i, b)[:, None]
Yx = Y - Xb_j
G = self.func(bw,
endog=Yx,
exog=-Z,
data_predict=-self.exog_nonparametric[ii, :])[0]
lt = Xb[ii, :] #.sum() # linear term
L += (self.endog[ii] - lt - G)**2
return L
def cv_loo(self, params):
"""
Similar to the cross validation leave-one-out estimator.
Modified to reflect the linear components.
Parameters
----------
params: array_like
Vector consisting of the coefficients (b) and the bandwidths (bw).
The first ``k_linear`` elements are the coefficients.
Returns
-------
L: float
The value of the objective function
References
----------
See p.254 in [1]
"""
params = np.asarray(params)
b = params[0 : self.k_linear]
bw = params[self.k_linear:]
LOO_X = LeaveOneOut(self.exog)
LOO_Y = LeaveOneOut(self.endog).__iter__()
LOO_Z = LeaveOneOut(self.exog_nonparametric).__iter__()
Xb = np.dot(self.exog, b)[:,None]
L = 0
for ii, X_not_i in enumerate(LOO_X):
Y = LOO_Y.next()
Z = LOO_Z.next()
Xb_j = np.dot(X_not_i, b)[:,None]
Yx = Y - Xb_j
G = self.func(bw, endog=Yx, exog=-Z,
data_predict=-self.exog_nonparametric[ii, :])[0]
lt = Xb[ii, :] #.sum() # linear term
L += (self.endog[ii] - lt - G) ** 2
return L