Independent, Identically Distributed Observations

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, …, X _n all 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.”