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

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

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Year of publication:	2000
Authors:	Butucea, Cristina
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 47.2000, 1, p. 85-90
Publisher:	Elsevier
Keywords:	Sobolev classes Minimax risk Adaptive density estimation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005074594