Function OPTwei transforms vector u as follows Remark: Yohai and Zamar (1997) showed that the optimal $\rho$ function is optimal in the following highly desirable sense: the final M estimate has a breakdown point of one-half and minimizes the maximum bias under contamination distributions (locally for small fraction of contamination), subject to achieving a desidered nominal asymptotic efficiency when the data are Gaussian.

\[ \psi(x) =\rho' (x) = \begin{cases} \frac{2.7692 }{c^2} \qquad |x| \leq \frac{2}{3} c \\ -\frac{5.3834 }{c^2} +\frac{43.0672 x^2}{c^4} -\frac{69.9840 x^4}{c^6} +\frac{32.3 x^6}{c^8} \qquad \frac{2}{3} c < |x| \leq c \\ 0 & \; \vert x \vert > c. \end{cases} \]