Ononot — Consider a non-regular case for MLE where the density f(x|\t

Inferential Statisticshard

0:00.0

Consider a non-regular case for MLE where the density $f(x|\theta) = 1$ for $\theta - 1/2 < x < \theta + 1/2$ . What is the asymptotic behavior of the MLE $\hat{\theta}_n$ ?