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Uniform Strong Consistency of Rao-Blackwell Distribution Function Estimators

Federico J. O'Reilly and C. P. Quesenberry
The Annals of Mathematical Statistics
Vol. 43, No. 5 (Oct., 1972), pp. 1678-1679
Stable URL: http://www.jstor.org/stable/2240091
Page Count: 2
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Abstract

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.

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