statsmodels.robust.norms.TukeyQuartic.rho#

TukeyQuartic.rho(z)[source]#

The robust criterion function for TukeyQuartic norm

Parameters:
zarray_like

1d array

Returns:
rhondarray

The value of the robust criterion function.

\[\begin{split}\rho(z) = \begin{cases} \frac{1}{2} z^2 \left(1 - \frac{4}{k + 2} x^k + \frac{1}{k + 1} x^{2k}\right) & \text{if } \lvert z \rvert \le c \\ \rho(c) & \text{if } \lvert z \rvert > c \end{cases}\end{split}\]

where \(x = z / c\).