Consider $n$ iid observations $X_1,X_2,\dots ,X_n$ from a $Uniform(a,b)$ distribution, where $a$ and $b$ are both unknown. How do we construct a joint confidence interval for $(a,b)$?
I would prefer a rectangular shape confidence interval, which can be obtained by using Bonferroni's method, so I guess the question can also be reformed as: How do we get a confidence interval for $a$?