I was wondering if anybody could help me here. I do not have access to a mathematical professor, and learn everything on my own. My question deals with the interpretation/definition of a sufficient statistic. I often see people saying things like "in terms of estimation, having the sufficient statistic is just as good as having the entire sample."
Fine, but what is referred to here when we say estimation? Is this always in terms of maximum liklihood estimation? Thanks!
No, UMVUE is also a function of the minimal sufficient statistic. MLE is always a function of the minimal sufficient statistic. Basically, I would dare to say that any good estimator (excluding some pathological cases) will be a function of he minimal sufficient statistic.