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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  7. N. G. de Bruijn, On some multiple integrals involving determinants, J. Indian Math. Soc. (N.S.) 19 (1955), 133-151 (1956) Zbl0068.24904MR79647
  8. Reinhard Hochmuth, Wavelet characterizations for anisotropic Besov spaces, Appl. Comput. Harmon. Anal. 12 (2002), 179-208 Zbl1003.42024MR1884234
  9. J. Ben Hough, Manjunath Krishnapur, Yuval Peres, Bálint Virág, Determinantal processes and independence, Probab. Surv. 3 (2006), 206-229 Zbl1189.60101MR2216966
  10. J. Ben Hough, Manjunath Krishnapur, Yuval Peres, Bálint Virág, Zeros of Gaussian analytic functions and determinantal point processes, 51 (2009), American Mathematical Society, Providence, RI Zbl1190.60038MR2552864
  11. Russell Lyons, Determinantal probability measures, Publ. Math. Inst. Hautes Études Sci. (2003), 167-212 Zbl1055.60003MR2031202
  12. Saunders Mac Lane, Garrett Birkhoff, Algebra, (1988), Chelsea Publishing Co., New York Zbl0641.12001MR941522

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