In the independent sampling model, Rao-Blackwell distribution function estimators F̃ₙ(x) obtained by conditioning on sufficient statistics Tₙ(X₁, ⋯, Xₙ) are considered. If for each n 1, Tₙ is symmetric in X₁,⋯, Xₙ and Tₙ₊₁ is B(Tₙ, Xₙ₊₁) measurable, it is shown that F̃ₙ(x) converges strongly to the corresponding $F(x)$ and uniformly in x. This is a direct generalization of the Glivenko-Cantelli theorem.
No takes yet. Share an insight, caveat, or question.
O'Reilly et al. (1972) studied this question.