statsmodels.robust.norms.TukeyBiweight

class statsmodels.robust.norms.TukeyBiweight(c=4.685)

Tukey’s biweight function for M-estimation

Parameters:

cfloat or array_like, optional

The tuning constant for Tukey’s Biweight. It has to be positive. An array is used element-wise, broadcast with the argument of the methods. The default value is c = 4.685.

Methods

__call__(z)

Return the value of estimator rho applied to an input

Raises:

TypeError

If c is not a real number or an array of real numbers.

ValueError

If c or any element of c is not positive, or is nan.

Notes

Tukey’s biweight is sometimes called bisquare.

Changed in version 0.15.1: The tuning constant is validated. Zero, negative and nan values raise a ValueError instead of creating a degenerate norm.

The tuning constant is validated when the norm is created and in _set_tuning_param. Plain attribute assignment after construction, norm.c = value, is not validated.

Methods

get_tuning([bp, eff])	Tuning parameter for given breakdown point or efficiency
max_rho()
psi(z)	The psi function for Tukey's biweight estimator
psi_deriv(z)	The derivative of Tukey's biweight psi function
rho(z)	The robust criterion function for Tukey's biweight estimator
weights(z)	Tukey's biweight weighting function for the IRLS algorithm

Properties

continuous
redescending