Estimation of the density of a determinantal process

Yannick Baraud[1]

  • [1] Université Nice Sophia Antipolis, CNRS, LJAD, UMR CNRS 7351, 06100 Nice, France

Confluentes Mathematici (2013)

  • Volume: 5, Issue: 1, page 3-21
  • ISSN: 1793-7434

Abstract

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We consider the problem of estimating the density Π of a determinantal process N from the observation of n independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when n goes to infinity, uniform rates of convergence over classes of densities Π of interest.

How to cite

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Baraud, Yannick. "Estimation of the density of a determinantal process." Confluentes Mathematici 5.1 (2013): 3-21. <http://eudml.org/doc/275497>.

@article{Baraud2013,
abstract = {We consider the problem of estimating the density $\Pi $ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when $n$ goes to infinity, uniform rates of convergence over classes of densities $\Pi $ of interest.},
affiliation = {Université Nice Sophia Antipolis, CNRS, LJAD, UMR CNRS 7351, 06100 Nice, France},
author = {Baraud, Yannick},
journal = {Confluentes Mathematici},
keywords = {Determinantal process - Density estimation- Oracle inequality - Hellinger distance; determinantal process; density estimation; oracle inequality; Hellinger distance},
language = {eng},
number = {1},
pages = {3-21},
publisher = {Institut Camille Jordan},
title = {Estimation of the density of a determinantal process},
url = {http://eudml.org/doc/275497},
volume = {5},
year = {2013},
}

TY - JOUR
AU - Baraud, Yannick
TI - Estimation of the density of a determinantal process
JO - Confluentes Mathematici
PY - 2013
PB - Institut Camille Jordan
VL - 5
IS - 1
SP - 3
EP - 21
AB - We consider the problem of estimating the density $\Pi $ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when $n$ goes to infinity, uniform rates of convergence over classes of densities $\Pi $ of interest.
LA - eng
KW - Determinantal process - Density estimation- Oracle inequality - Hellinger distance; determinantal process; density estimation; oracle inequality; Hellinger distance
UR - http://eudml.org/doc/275497
ER -

References

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