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

Cristina Butucea

Statistics & Probability Letters, 2000, vol. 47, issue 1, 85-90

Abstract: 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.

Keywords: Sobolev; classes; Minimax; risk; Adaptive; density; estimation (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (2)

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