What if we need to look for a sufficient statistic. We do the maths and we end up with a specific formule (with help of the factorization criterion) and we have the random variables X,i bounded; 0 < X,i < THETA.
Which can be written with order statistics as follows: 0 < X(1) =< X(n) < 0.
So why do we choose X(n) to be sufficient? Can all the other order statistic also be efficient? My book just picks X(n) as sufficient statistic without telling me about the others, which I think could also be sufficient.