Huber k estimator

Course of the ρ function of the Huber k estimator for k = 1.28

The Huber k estimator is a special estimator for M-estimators ( robust estimation methods ). It is used to estimate the location parameter of a normally distributed population.

${\displaystyle \rho (z)}$	${\displaystyle \psi (z)}$
${\displaystyle \rho (z)_{H}={\begin{cases}{\frac {1}{2}}z^{2}&|z|\leq {}k\\k|z|-{\frac {1}{2}}k^{2}&|z|>k\end{cases}}}$	${\displaystyle \psi (z)_{H}={\begin{cases}z&|z|\leq {}k\\k\operatorname {sgn} (z)&|z|>k\end{cases}}}$

The idea behind this is that large values ​​that are viewed as outliers should no longer have a quadratic influence above a certain size . ${\displaystyle k}$

${\displaystyle k}$is a so-called tuning constant. The most common value is what the 0.9 quantile of the standardized normal distribution corresponds to. ${\displaystyle k=1{,}28}$

literature

• Joachim Hartung, Bärbel Elpelt, Karl-Heinz Klösener: Statistics: Teaching and manual of applied statistics . Oldenbourg Verlag, Munich / Vienna 2002, pp. 869–872