

\subsection{\bf Robust Determination of Mean---I}

\begin{slide}
\begin{itemize}
\item The first book cited (Andrews) has an instructive study of a very
simple problem.

\item Given a univariate sample $\lbrace x^{(i)}\ \ i=1,\ \ N\rbrace$
from some distribution,

\item Find an estimate of the mean $\mu$ of the underlying probability
distribution.

\item The natural method is to estimate $\mu$ from the arithmetic mean
\[
\mu^*_{Am} = \frac{1}{N} \sum^N_{i=1} x^{(i)}
\]

\item As long as the underlying distribution has a finite Standard
Deviation, this will have an error $\propto \frac{1}{\sqrt{N}}$ which
$\rightarrow 0$ as $N\rightarrow\infty$.
\end{itemize}
\end{slide}

