Independent, Identically Distributed Observations

Abstract

The structure that has received by far the most attention in the statistical literature is one that can be described as follows. One takes a family of probability measures { p$θ$: $θ$ ∈ $Θ$ }on some space (X, A). Then one considers experiments $ε$n= { P$θ$, n; $θ$ ∈ $Θ$ }where P$θ$, n is the joint distribution of n observations X1, X2, …, Xnall independent with individual distribution p$θ$. One studies the asymptotic behavior of the system as n tends to infinity. We shall refer to this as the ``standard i.i.d. case.''