Curious how people are ‘applying’ the Law of Large Numbers in a way that needs this advice to be tacked on?
> Always keep the speed of convergence in mind when applying the law of large numbers.
Any ‘application’ of the LLN basically amounts to replacing some probalistic number derived from a bunch of random samples with the expected value of that number… and tacking on ‘for sufficiently large n’ as a caveat to your subsequent conclusions.
Figuring out whether, in practical cases, you will have a sufficiently large n that the conclusion is valid is a necessary step in the analysis.
> Figuring out whether, in practical cases, you will have a sufficiently large n that the conclusion is valid is a necessary step in the analysis.
The econometrics textbook I studied has more words “asymptotic” in it than there are pages. Oftentimes it’s impractical or even theoretically intractable to derive finite sample properties (and thus to answer when n is really large enough).
> Always keep the speed of convergence in mind when applying the law of large numbers.
Any ‘application’ of the LLN basically amounts to replacing some probalistic number derived from a bunch of random samples with the expected value of that number… and tacking on ‘for sufficiently large n’ as a caveat to your subsequent conclusions.
Figuring out whether, in practical cases, you will have a sufficiently large n that the conclusion is valid is a necessary step in the analysis.