

\subsection{\bf Comparison of Moment Method}
\subsection{\bf with Maximum Likelihood---II}

\begin{slide}
\begin{itemize}
\item The value of $\frac{1}{N\sigma^2}\big\vert_{m.l.m.}$ is equal to
$\frac{1}{N\sigma^2}\big\vert_1$ value when $a=0$

\item but
\[
\frac{1}{\lbrack N\sigma^2 \rbrack}\big\vert_{m.l.m.} = \infty\ \mbox{when}\
a=\pm 1 .
\]

\item So
\begin{eqnarray*} 
\sigma^2 \big\vert_{m.l.m.} & = & \sigma^2 \big\vert_1 \hspace{1em} a
= 0 \\
& < & \sigma^2 \vert_1 \hspace{1em} a\neq 0 .
\end{eqnarray*}

\item i.e., maximum likelihood is always better, or as good as, moment
method---in agreement with general theorem.
\end{itemize}
\end{slide}

