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M Banerjee 著2010 — Theorem 1.1 Let F be a class of measurable functions with N[] (ϵ,F ) < ∞ for all ϵ > 0. Then. F is P-Glivenko-Cantelli, i.e.. Pn − P⋆.
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And it suffices to show: sup f∈F. |R(f) − ˆR(f)| is small. For GC class functions this sufficient condition is ... Glivenko-Cantelli Theorem ⇐⇒ ∀P, sup.
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P Bartlett 著 — Definition: F is a Glivenko-Cantelli class for P if sup f∈F ... indexed by a class of functions F, and Pn − PF := sup f∈F. |Pnf − Pf|.
G SUZUKI 著被引用数: 4 — Let (2, 4, P) be a probability space and $=($,$", ..., *) a k di- ... we shall say that the pair (F, 6) belongs to the Glivenko-Cantelli class.
C Caramanis 著2000 — Moreover, if J is a universal Glivenko–Cantelli class, and furthermore the rate of convergence of the empirical measure is uniform over all P ∈ ...
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N Alon 著2017被引用数: 8 — In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which ... The above theorems show that, with high probability, F and Fn are close ...
A van der Vaart 著被引用数: 121 — ABSTRACT We show that the P−Glivenko property of classes of functions ... in this case we say that F is a strong Glivenko-Cantelli class for P. Useful.
family F is said to be a µ-Glivenko-Cantelli class (cf. ... 225 and p. ... Adams and Nobel [2] showed that Vapnik-Chervonenkis classes of sets are uni-.
Evarist Giné、 David M. Mason、 Jon A. Wellner — 2012Mathematics
Furthermore, it suffices to show that p(F1 ... Any strong P-Glivenko Cantelli class F is totally bounded in L1(P) if and only if ||P||+ 4 co.

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