Consider the uniform distribution on

Define (i.e. the geometric mean) and the Ys are independent rvs.

Is a sufficient estimator?

I just really have a hard time with the concept of sufficiency. I basically just try to use the factorization theorem without understanding what I'm doing, and I am struggling to do so with the geometric mean. I was thinking to use an indicator function for y from 0 to theta?

EDIT: Maybe I am having trouble because it is not sufficient. It seems like averages are not going to tell all the information relevant to find upper bounds.