

\subsection{\bf Particular Robust Estimates for}
\subsection{\bf Likelihood---Andrews}

\begin{slide}
\begin{itemize}
\item Many forms for $\Psi$ have been proposed.  

\item The most successful was that due to Andrews with

\vspace*{10pt}
\centerline{\psfig{figure=fig27.phys.ps,clip=true,width=5.0in}}
\vspace*{10pt}

\begin{tabular}{ll}
$\Psi(z) = \sin (z/2.1)$ & $\vert z \vert < 2.1 \pi$ \\
\phantom{$\Psi(z)$} $ = 0$ & $\vert z \vert \ge 2.1 \pi$ 
\end{tabular}
\vspace{10pt}

\item Note $z$ is $\frac{(x-\mu)}{\sigma}$ where $\sigma$ supplies
natural scale for problem.

\item We do not need a very good estimate for $\sigma$ but it should be
robust!

\item A simple choice is $\sigma = \mbox{mean} \vert x^{(i)} - \mu
\vert$ which formula is applied iteratively as value of $\mu$ is
refined.
\end{itemize}
\end{slide}

