statsmodels.robust.norms.TukeyQuartic

class statsmodels.robust.norms.TukeyQuartic(c=3.61752, k=4)

Variant of Tukey’s biweight function with power 4 for M-estimation

Parameters:

cfloat, optional

The tuning constant for Tukey’s Biweight. It has to be positive. The default value is c = 3.61752.

kint, optional

The power used in the inner term in place of the power 2 used by Tukey’s biweight. It has to be a positive, even integer, because psi is an odd function only for even powers. The default value is 4.

Methods

__call__(z)

Return the value of estimator rho applied to an input

Raises:

TypeError

If c is not a real number, or k is not an integer.

ValueError

If c is not positive or is nan, or if k is not positive and even.

Notes

This is a variation of Tukey’s biweight (bisquare) function where the weight function has power 4 instead of power 2 in the inner term.

The default value of c is only valid for k = 4, it needs to be changed for other powers.

Changed in version 0.15.1: The tuning constant c and the power k are validated. Invalid values raise a TypeError or ValueError instead of creating a degenerate norm.

The constants are validated when the norm is created and in _set_tuning_param. Plain attribute assignment after construction, for example norm.c = value, is not validated.

Methods

max_rho()
psi(z)	The psi function of TukeyQuartic norm
psi_deriv(z)	The derivative of the TukeyQuartic psi function
rho(z)	The robust criterion function for TukeyQuartic norm
weights(z)	TukeyQuartic weighting function for the IRLS algorithm

Properties

continuous
redescending