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The pointwise rate of convergence of the kernel regression estimate

✍ Scribed by Adam Krzyzak; Mirosław Pawlak


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
357 KB
Volume
16
Category
Article
ISSN
0378-3758

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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