

\subsection{\bf Theorem on Asymptotic Validity}
\subsection{\bf of Maximum Likelihood}
\subsection{\bf Method---Conditions and}
\subsection{\bf Statement of Theorem}

\begin{slide}
\begin{itemize} 
\item This is described in Cramer Chapters 22 and 23

\item {\bf Theorem:}

Let $P(x_i, \alpha)$ be a normalized probability for a result $x_i$
given theoretical parameter $\alpha$.  We have $n$ such observations
$x_i$:

\begin{description}
\item{$\bullet$} $L = {\displaystyle \Pi^n_{i=1}} P(x_i , \alpha)$ is
usual likelihood function.
\item{$\bullet$} Let $\alpha^*$ be maximum of $L$ with respect to $\alpha$.
\item{$\bullet$} There are three basic results that can be proven.
\end{description}
\end{itemize}
\end{slide}

