# Maximum Likelihood Estimator

1. Dec 3, 2009

### cse63146

1. The problem statement, all variables and given/known data

Let Y1<Y2<...<Yn be the order statistics of a random sample from a distribution with pdf $$f(x; \theta) = 1$$, $$\theta - 0.5 < x < \theta + 0.5$$. Show that every statistic u(X1,X2,...,Xn) such that $$Y_n - 0.5<u(X_1,X_2,...,X_n)<Y_1 + 0.5$$ is a mle of theta. In particular $$(4Y_1 + 2Y_n + 1)/6, (Y_1 + Y_n)/2, (2Y_1 + 4Y_n - 1)/6$$ are three such statistics.

2. Relevant equations

3. The attempt at a solution

I don't even know how to start this problem. Can someone please point me in the right direction?