

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

\begin{slide}
\begin{itemize}
\item An interesting class of robust estimators are based on the
modification of the maximum likelihood equations.  

\item Thus, let
\[
z^{(i)} = \frac{\left( x^{(i)} - \mu \right)}{\sigma}
\]
and suppose that $p(x,\mu )$ is just a function of $z$.  (True for
Gaussian case!).  

\item The likelihood equation for $\mu$ is
\[
\frac{\partial}{\partial\mu} \ln L = 0
\]
or
\[
\sum^N_{i=1} \frac{\partial}{\partial\mu} \ln p 
\left( \frac{\left( x^{(i)} - \mu \right)}{\sigma} \right) = 0
\]
\end{itemize}
\end{slide}

