I'm lecturing on suff stats on monday.
The point is that the indicator function is 0 or 1.
It's 1 as long as each X_i is between 0 and theta.
NOW look at the order stats
YOU need to convince yourself that
0<X_1,...., X_n<theta here these are the unordered data
is the same as
which is the same as
All we need is the largest to be less than theta
Now if theta was a lower value for our rvs instead of an upper bound,
then the smallest order stat would be suff for theta
And in the case of U(a,b)
the smallest and largest order stats are suff for the TWO
parameters, a and b.
ARE you using Wackerly too?
I knew Dennis at Florida and Scheaffer was my chair there.