I have a problem with the scale uniform interval estimator (Example 9.1.6, page 419, Casella-Berger). Let $X_1,\dots,X_n \sim \text{IID U}(0,\theta)$ be our observed data. We are interested in an interval estimator of $\theta$.
Consider the interval estimator $[Y + c; Y + d]$ where $Y = \max (X_1,\dots,X_n)$ and $0<c<d$ (note that $\theta$ is necessarily larger than $y$). I have no problem with the solution but I don't understand why we consider the interval $Y + c$ instead of $Y -c$.