M-estimators
\[\rho(x)=\frac{1}{2}x^2\]
\[\rho(x)=|x|\]
\[\rho(x)=\frac{1}{2}x^2~ 1\{|x| \leq c\}\]
\[\rho(x)= \left\{
\begin{array}{ll}\frac{1}{2}x^2, & |x| \leq c\\
c(|x|-\frac{1}{2}c), & |x|>c
\end{array}
\right.\]
\[\psi(x)= sign(x)\cdot\left\{
\begin{array}{ll}
|x|, & |x|<c_1 \\
c_1, & c_1 \leq |x| \leq c_2 \\
\frac{c_1(c_3-|x|)}{c_3-c_2}, & c_2 < |x| < c_3 \\
0, & |x| \geq c_3
\end{array} \right.\]
\[w(x)=\left(1-\left(\frac{x}{c}\right)^2\right)_+^2\]