Why MLE for uniform distribution doesn't have usual properties?

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I am now struggling with a problem

distribution of $x$ is $f(x) = 1/\theta $, $0 \leq x \leq \theta$. We have a random sample from this distribution. Calculate MLE for $\theta$ and explain why some properties of MLE doesn't hold here.

I have shown $\max _{1 \leq i \leq n} X_{i}$ is the MLE of the uniform distribution, but I don't know why some properties of MLE doesn't hold here. I think it has something to do with the regular assumptions on the distribution. Could someone help me with it?

Thanks in advance!