Math 6010 • Linear Models

Let \(X_1,X_2,\ldots,X_n\) be independent identically distributed random variables, uniformly distributed on \([0,\theta]\), \(\theta>\theta_0\). We want to test \(H_0:\theta=\theta_0\) against \(H_A:\theta>\theta_0\).
\begin{parts}
\item Find the uniformly most powerful test. (You must prove your claim.)
\item Show that the uniformly most powerful test and the likelihood ratio test are equivalent.
\item Compute the power function of the most powerful test.
\end{parts}