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The adaptive rate of convergence in a problem of pointwise density estimation

✍ Scribed by Cristina Butucea

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 90 KB
Volume: 47
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(99)00141-8

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✦ Synopsis

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 adaptive.

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