Let Y1 < Y2 < ... < Yn be the order statistics of a random sample of size n from the uniform distribution of the continuous type over the closed interval: $$[\theta - \rho, \theta + \rho]$$ Find the maximum likelihood estimators for $\theta$ and $\rho$. Are these two unbiased estimators?
Can anyone help with this problem? It looks like my one weakness with MLE is figuring them out when order statistics are introduced. Moreover, I have no idea how to determine if they're unbiased (I can't even figure out the respective pdf's-which I definitely need right?). I'd really appreciate any help someone can offer.