Source code for statsmodels.nonparametric.bandwidths

import numpy as np
from scipy.stats import scoreatpercentile as sap

from statsmodels.compat.pandas import Substitution
from statsmodels.sandbox.nonparametric import kernels

def _select_sigma(X):
    """
    Returns the smaller of std(X, ddof=1) or normalized IQR(X) over axis 0.

    References
    ----------
    Silverman (1986) p.47
    """
#    normalize = norm.ppf(.75) - norm.ppf(.25)
    normalize = 1.349
#    IQR = np.subtract.reduce(percentile(X, [75,25],
#                             axis=axis), axis=axis)/normalize
    IQR = (sap(X, 75) - sap(X, 25))/normalize
    return np.minimum(np.std(X, axis=0, ddof=1), IQR)


## Univariate Rule of Thumb Bandwidths ##
[docs]def bw_scott(x, kernel=None): """ Scott's Rule of Thumb Parameters ---------- x : array_like Array for which to get the bandwidth kernel : CustomKernel object Unused Returns ------- bw : float The estimate of the bandwidth Notes ----- Returns 1.059 * A * n ** (-1/5.) where :: A = min(std(x, ddof=1), IQR/1.349) IQR = np.subtract.reduce(np.percentile(x, [75,25])) References ---------- Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. """ A = _select_sigma(x) n = len(x) return 1.059 * A * n ** (-0.2)
[docs]def bw_silverman(x, kernel=None): """ Silverman's Rule of Thumb Parameters ---------- x : array_like Array for which to get the bandwidth kernel : CustomKernel object Unused Returns ------- bw : float The estimate of the bandwidth Notes ----- Returns .9 * A * n ** (-1/5.) where :: A = min(std(x, ddof=1), IQR/1.349) IQR = np.subtract.reduce(np.percentile(x, [75,25])) References ---------- Silverman, B.W. (1986) `Density Estimation.` """ A = _select_sigma(x) n = len(x) return .9 * A * n ** (-0.2)
def bw_normal_reference(x, kernel=kernels.Gaussian): """ 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. 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.` """ C = kernel.normal_reference_constant A = _select_sigma(x) n = len(x) return C * A * n ** (-0.2) ## Plug-In Methods ## ## Least Squares Cross-Validation ## ## Helper Functions ## bandwidth_funcs = { "scott": bw_scott, "silverman": bw_silverman, "normal_reference": bw_normal_reference, }
[docs]@Substitution(", ".join(sorted(bandwidth_funcs.keys()))) def select_bandwidth(x, bw, kernel): """ Selects bandwidth for a selection rule bw this is a wrapper around existing bandwidth selection rules Parameters ---------- x : array_like Array for which to get the bandwidth bw : str name of bandwidth selection rule, currently supported are: %s kernel : not used yet Returns ------- bw : float The estimate of the bandwidth """ bw = bw.lower() if bw not in bandwidth_funcs: raise ValueError("Bandwidth %s not understood" % bw) #TODO: uncomment checks when we have non-rule of thumb bandwidths for diff. kernels # if kernel == "gauss": return bandwidth_funcs[bw](x, kernel)
# else: # raise ValueError("Only Gaussian Kernels are currently supported")