With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

7.1. Generalities

Asymptotic statistics is the study of decision rules when the number of observations tends to infinity.

Theoretically, the asymptotic model may be described as follows: one considers a statistical model written as , a sequence of sub-σ-algebras of , and a sequence (dn, n ≥ 1) of -adapted decision rules (i.e. dn is -measurable for all n ≥ 1).

The decision space being provided with a distance δ, we say that (dn) is convergent in probability if: where aθ denotes the “correct” decision when the value of the parameter is θ.

In the usual case, where (Xn,n ≥ 1) is a sample from Pθ, θ ∈ Θ, we have , , and , and the convergence in probability may be rewritten ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required