The adaptive rate of convergence in a pr
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Cristina Butucea
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Article
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2000
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Elsevier Science
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English
β 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