A Likelihood Ratio Test for the Endpoint
Let $X_1,X_2,X_3$ be independent uniform on $[0,\theta]$. To test $H_0:\theta=1$ against $H_1:\theta\ne1$, use the likelihood ratio statistic $\Lambda=\dfrac{\sup_{\theta=1}L(\theta)}{\sup_{\theta>0}L(\theta)}$ and reject when $\Lambda\le 1/8$. Find the probability that this test rejects when the true parameter is $\theta=3/2$. Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Power of a One-Sided Uniform Test 2.0/10
- Power of a Ten-Flip Test 2.0/10
Source: Original problem written for AxiomIQ. Illustrates a non-regular case where Wilks' theorem does not apply.