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Pointwise convergence of partial functions: The Gerlits–Nagy Problem

✍ Scribed by Tal Orenshtein; Boaz Tsaban


Book ID
119183713
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
277 KB
Volume
232
Category
Article
ISSN
0001-8708

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The adaptive rate of convergence in a pr
✍ Cristina Butucea 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 90 KB

We estimate the common density function of n i.i.d. observations, at a ÿxed point, over Sobolev classes of functions having regularity ÿ. We prove that the optimal rate of convergence cannot be attained in adaptive estimation, i.e. uniformly over ÿ in some interval B n. A slower rate is shown to be