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The Density of Weakly Complete Problems under Adaptive Reductions

✍ Scribed by Lutz, Jack H.; Zhao, Yong


Book ID
118178222
Publisher
Society for Industrial and Applied Mathematics
Year
2000
Tongue
English
Weight
185 KB
Volume
30
Category
Article
ISSN
0097-5397

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The adaptive rate of convergence in a pr
✍ Cristina Butucea πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 90 KB

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