

\subsection{\bf Likelihood Based Robust}
\subsection{\bf Estimation of Means---II}

\begin{slide}
\begin{itemize}
\item Now, as we are assuming $p$ to be an even function of $z$, i.e.,
symmetric about the mean, we write the above as
\begin{equation}
\sum^N_{i=1} \Psi \left( \frac{\left( x^{(i)} - \mu \right)}{\sigma} 
\right) = 0
\end{equation}

\item where $\Psi$ is an {\em odd\/} function of its argument.

\item For the case of Gaussian $p$, 

\item $\Psi$ is just $(x^{(i)}-\mu)/\sigma^2$ and Equation~(37) is
\[
\frac{1}{\sigma^2} \sum^N_{i=1} \left( x^{(i)} - \mu^*_L \right) = 0
\]

\item which gives the arithmetic mean as the maximum likelihood
estimate of the mean.
\end{itemize}
\end{slide}

