Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

doi:10.1051/ps/2010012

Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

Université de Toulouse

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

Abstract

We build confidence balls for the common density s of a real valued sample X₁, …, X_n. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

Original language	English
Pages (from-to)	61-85
Number of pages	25
Journal	ESAIM - Probability and Statistics
Volume	16
DOIs	https://doi.org/10.1051/ps/2010012
Publication status	Published - 1 Jan 2012
Externally published	Yes

Keywords

Confidence balls
Density estimation
Resampling methods

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10.1051/ps/2010012

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abstract = "We build confidence balls for the common density s of a real valued sample X1, …, Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.",

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AB - We build confidence balls for the common density s of a real valued sample X1, …, Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

KW - Confidence balls

KW - Density estimation

KW - Resampling methods

U2 - 10.1051/ps/2010012

DO - 10.1051/ps/2010012

M3 - Article

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SP - 61

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JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

ER -

Adaptive non-asymptotic confidence balls in density estimation

Abstract

Keywords

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