# Is there a statistical application that requires strong consistency?

I was wondering if someone knows or if there exists an application in statistics in which strong consistency of an estimator is required instead of weak consistency. That is, strong consistency is essential for the application and the application would not work with weak consistency.

• No, there is no such application. – kjetil b halvorsen Oct 29 '13 at 20:58
• Sometimes I wonder if even weak consistency - outside its intuitive appeal - is in reality very important. If I have an estimator that behaves very sensibly at every finite sample size below $n=10^{1000}$ and in reality my biggest sample size will only ever be a miniscule fraction of that, I might have an inconsistent estimator that's nevertheless perfectly fine. It seems to me that the actual value in consistency at all is that it's usually (in practical cases rather than pathological ones) associated with estimators that still behave 'nicely' as sample sizes move past what we might ever see. – Glen_b -Reinstate Monica Nov 1 '13 at 23:23