def cv_loo(self, bw, func):
"""
The cross-validation function with leave-one-out
estimator
Parameters
----------
bw: array_like
Vector of bandwidth values
func: callable function
Returns the estimator of g(x).
Can be either ``_est_loc_constant`` (local constant) or
``_est_loc_linear`` (local_linear).
Returns
-------
L: float
The value of the CV function
Notes
-----
Calculates the cross-validation least-squares
function. This function is minimized by compute_bw
to calculate the optimal value of bw
For details see p.35 in [2]
..math:: CV(h)=n^{-1}\sum_{i=1}^{n}(Y_{i}-g_{-i}(X_{i}))^{2}
where :math:`g_{-i}(X_{i})` is the leave-one-out estimator of g(X)
and :math:`h` is the vector of bandwidths
"""
LOO_X = LeaveOneOut(self.exog)
LOO_Y = LeaveOneOut(self.endog).__iter__()
LOO_W = LeaveOneOut(self.W_in).__iter__()
L = 0
for ii, X_not_i in enumerate(LOO_X):
Y = LOO_Y.next()
w = LOO_W.next()
G = func(bw, endog=Y, exog=-X_not_i,
data_predict=-self.exog[ii, :], W=w)[0]
L += (self.endog[ii] - G) ** 2
# Note: There might be a way to vectorize this. See p.72 in [1]
return L / self.nobs
def loo_likelihood(self, bw, func=lambda x: x):
"""
Returns the leave-one-out conditional likelihood of the data.
If `func` is not equal to the default, what's calculated is a function
of the leave-one-out conditional likelihood.
Parameters
----------
bw: array_like
The bandwidth parameter(s).
func: callable, optional
Function to transform the likelihood values (before summing); for
the log likelihood, use ``func=np.log``. Default is ``f(x) = x``.
Returns
-------
L: float
The value of the leave-one-out function for the data.
Notes
-----
Similar to ``KDE.loo_likelihood`, but substitute ``f(y|x)=f(x,y)/f(y)``
for ``f(x)``.
"""
yLOO = LeaveOneOut(self.data)
xLOO = LeaveOneOut(self.exog).__iter__()
L = 0
for i, Y_j in enumerate(yLOO):
X_not_i = xLOO.next()
f_yx = gpke(bw,
data=-Y_j,
data_predict=-self.data[i, :],
var_type=(self.dep_type + self.indep_type))
f_x = gpke(bw[self.k_dep:],
data=-X_not_i,
data_predict=-self.exog[i, :],
var_type=self.indep_type)
f_i = f_yx / f_x
L += func(f_i)
return -L
def loo_likelihood(self, bw, func=lambda x: x):
"""
Returns the leave-one-out conditional likelihood of the data.
If `func` is not equal to the default, what's calculated is a function
of the leave-one-out conditional likelihood.
Parameters
----------
bw: array_like
The bandwidth parameter(s).
func: callable, optional
Function to transform the likelihood values (before summing); for
the log likelihood, use ``func=np.log``. Default is ``f(x) = x``.
Returns
-------
L: float
The value of the leave-one-out function for the data.
Notes
-----
Similar to ``KDE.loo_likelihood`, but substitute ``f(y|x)=f(x,y)/f(y)``
for ``f(x)``.
"""
yLOO = LeaveOneOut(self.data)
xLOO = LeaveOneOut(self.exog).__iter__()
L = 0
for i, Y_j in enumerate(yLOO):
X_not_i = xLOO.next()
f_yx = gpke(bw, data=-Y_j, data_predict=-self.data[i, :],
var_type=(self.dep_type + self.indep_type))
f_x = gpke(bw[self.k_dep:], data=-X_not_i,
data_predict=-self.exog[i, :],
var_type=self.indep_type)
f_i = f_yx / f_x
L += func(f_i)
return -L
