Details

Autor(en) / Beteiligte

• Landers, Dieter
• Rogge, Lothar

Titel

Second-Order Approximation in the Conditional Central Limit Theorem

Ist Teil von

• The Annals of probability, 1986-01, Vol.14 (1), p.313-325

Ort / Verlag

Hayward, CA: Institute of Mathematical Statistics

Erscheinungsjahr

1986

Link zum Volltext

Quelle

Project Euclid Complete

Beschreibungen/Notizen

• Let Xn, n ∈ N be i.i.d. with mean 0 and variance 1. Let B ∈ σ(Xn: n ∈ N) be a set such that its distances from the σ-fields σ(X1,⋯, Xn) are of order O(1/n(lg n)2 + ε) for some$\varepsilon > 0$. We prove that for those B the conditional probabilities$P((1/\sqrt n)\sum^n_{i=1} X_i \leq t\mid B)$can be approximated by a modified Edgeworth expansion up to order O(1/n). An example shows that this is not true any more if the distances of B from σ(X1,⋯, Xn) are only of order O(1/n(lg n)2).