Source code for statsmodels.nonparametric.bandwidths

import numpy as np
from scipy.stats import scoreatpercentile

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


def _select_sigma(x, percentile=25):
    """
    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 = (scoreatpercentile(x, 75) - scoreatpercentile(x, 25)) / normalize
    std_dev = np.std(x, axis=0, ddof=1)
    if IQR > 0:
        return np.minimum(std_dev, IQR)
    else:
        return std_dev


## 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=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) ## 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) bandwidth = bandwidth_funcs[bw](x, kernel) if np.any(bandwidth == 0): # eventually this can fall back on another selection criterion. err = "Selected KDE bandwidth is 0. Cannot estimate density. " \ "Either provide the bandwidth during initialization or use " \ "an alternative method." raise RuntimeError(err) else: return bandwidth

Last update: May 25, 2024