Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞.
In practice, a limit evaluation is considered to be approximately valid for large finite sample sizes too.
The law states that for a sequence of independent and identically distributed (IID) random variables X1, X2, ..., if one value is drawn from each random variable and the average of the first n values is computed as Xn, then the Xn converge in probability to the population mean E[Xi] as n → ∞.
[2] Besides the standard approach to asymptotics, other alternative approaches exist: In many cases, highly accurate results for finite samples can be obtained via numerical methods (i.e. computers); even in such cases, though, asymptotic analysis can be useful.
A primary goal of asymptotic analysis is to obtain a deeper qualitative understanding of quantitative tools.