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

Cristina Butucea

doi:10.1016/s0167-7152(99)00141-8

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

Cristina Butucea

Humboldt-Universität zu Berlin

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	85-90
Number of pages	6
Journal	Statistics and Probability Letters
Volume	47
Issue number	1
DOIs	https://doi.org/10.1016/s0167-7152(99)00141-8
Publication status	Published - 15 Mar 2000

Keywords

Adaptive density estimation
Minimax risk
Sobolev classes

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10.1016/s0167-7152(99)00141-8

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

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

KW - Adaptive density estimation

KW - Minimax risk

KW - Sobolev classes

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DO - 10.1016/s0167-7152(99)00141-8

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SP - 85

EP - 90

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 1

ER -

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

Abstract

Keywords

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