Math 6010 • Linear Models

Let \(X_1,X_2,\ldots,X_n\) be independent Poisson random variables with parameters \(\theta_1,\theta_2,\ldots,\theta_n\). We wish to test \(H_0:\theta_1=\theta_2=\cdots=\theta_n\) against the alternative that \(H_0\) is not true.
\begin{parts}
\item Find the likelihood ratio test. (5 points)
\item Show that the likelihood ratio is asymptotically normal (after centralizing and normalizing) under \(H_0\). (5 points)
\end{parts}