Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 61-85
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Lerasle, Matthieu. "Adaptive non-asymptotic confidence balls in density estimation." ESAIM: Probability and Statistics 16 (2012): 61-85. <http://eudml.org/doc/222474>.

@article{Lerasle2012,
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.},
author = {Lerasle, Matthieu},
journal = {ESAIM: Probability and Statistics},
keywords = {Confidence balls; density estimation; resampling methods; confidence balls},
language = {eng},
month = {7},
pages = {61-85},
publisher = {EDP Sciences},
title = {Adaptive non-asymptotic confidence balls in density estimation},
url = {http://eudml.org/doc/222474},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Lerasle, Matthieu
TI - Adaptive non-asymptotic confidence balls in density estimation
JO - ESAIM: Probability and Statistics
DA - 2012/7//
PB - EDP Sciences
VL - 16
SP - 61
EP - 85
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.
LA - eng
KW - Confidence balls; density estimation; resampling methods; confidence balls
UR - http://eudml.org/doc/222474
ER -

References

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