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On arbitrarily slow rates of global convergence in density estimation

✍ Scribed by Luc Devroye


Publisher
Springer
Year
1983
Tongue
English
Weight
372 KB
Volume
62
Category
Article
ISSN
1432-2064

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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