3.8.2.1.1. statsmodels.nonparametric.bandwidths.bw_normal_reference¶

statsmodels.nonparametric.bandwidths.bw_normal_reference(x, kernel=<class 'statsmodels.sandbox.nonparametric.kernels.Gaussian'>)[source]¶

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.