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A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences

✍ Scribed by Hao Yu


Publisher
Springer
Year
1993
Tongue
English
Weight
554 KB
Volume
95
Category
Article
ISSN
1432-2064

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Necessary and sufficient conditions for
✍ Dragan RaduloviΔ‡; Marten Wegkamp πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 200 KB

Let X 1 ; : : : ; X n be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator P n; H and establish weak convergence of the empirical process √ n(P n; H -P)(f) f∈F under sharp conditions. If