def test_bandwidth_zero(self):
kern = kernels.Gaussian()
for bw in ['scott', 'silverman', 'normal_reference']:
with pytest.raises(RuntimeError,
match="Selected KDE bandwidth is 0"):
select_bandwidth(self.xx, bw, kern)
def test_calculate_bandwidth_gaussian(self):
bw_expected = [
0.29774853596742024, 0.25304408155871411, 0.29781147113698891
]
kern = kernels.Gaussian()
bw_calc = [0, 0, 0]
for ii, bw in enumerate(['scott', 'silverman', 'normal_reference']):
bw_calc[ii] = select_bandwidth(Xi, bw, kern)
assert_allclose(bw_expected, bw_calc)
def bw_normal_reference(x, kernel=None):
"""
Plug-in bandwidth with kernel specific constant based on normal reference.
This bandwidth minimizes the mean integrated square error if the true
distribution is the normal. This choice is an appropriate bandwidth for
single peaked distributions that are similar to the normal distribution.
Parameters
----------
x : array_like
Array for which to get the bandwidth
kernel : CustomKernel object
Used to calculate the constant for the plug-in bandwidth.
The default is a Gaussian kernel.
Returns
-------
bw : float
The estimate of the bandwidth
Notes
-----
Returns C * A * n ** (-1/5.) where ::
A = min(std(x, ddof=1), IQR/1.349)
IQR = np.subtract.reduce(np.percentile(x, [75,25]))
C = constant from Hansen (2009)
When using a Gaussian kernel this is equivalent to the 'scott' bandwidth up
to two decimal places. This is the accuracy to which the 'scott' constant is
specified.
References
----------
Silverman, B.W. (1986) `Density Estimation.`
Hansen, B.E. (2009) `Lecture Notes on Nonparametrics.`
"""
if kernel is None:
kernel = kernels.Gaussian()
C = kernel.normal_reference_constant
A = _select_sigma(x)
n = len(x)
return C * A * n ** (-0.2)
class TestGau(CheckKernelMixin):
kern_name = 'gau'
kern = kernels.Gaussian()
class TestGaussian(CheckNormalReferenceConstant):
kern = kernels.Gaussian()
constant = 1.06
