# 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

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topBaraud, 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

top- N. Akakpo, Estimation adaptative par selection de partitions en rectangles dyadiques, (2009)
- Greg W. Anderson, Alice Guionnet, Ofer Zeitouni, An introduction to random matrices, 118 (2010), Cambridge University Press, Cambridge Zbl1184.15023MR2760897
- Jinho Baik, Eric M. Rains, Algebraic aspects of increasing subsequences, Duke Math. J. 109 (2001), 1-65 Zbl1007.05096MR1844203
- Yannick Baraud, Estimator selection with respect to Hellinger-type risks, Probab. Theory Related Fields 151 (2011), 353-401 Zbl05968717MR2834722
- Lucien Birgé, Model selection via testing: an alternative to (penalized) maximum likelihood estimators, Ann. Inst. H. Poincaré Probab. Statist. 42 (2006), 273-325 Zbl1333.62094MR2219712
- Alexei Borodin, Persi Diaconis, Jason Fulman, On adding a list of numbers (and other one-dependent determinantal processes), Bull. Amer. Math. Soc. (N.S.) 47 (2010), 639-670 Zbl1230.05292MR2721041
- N. G. de Bruijn, On some multiple integrals involving determinants, J. Indian Math. Soc. (N.S.) 19 (1955), 133-151 (1956) Zbl0068.24904MR79647
- Reinhard Hochmuth, Wavelet characterizations for anisotropic Besov spaces, Appl. Comput. Harmon. Anal. 12 (2002), 179-208 Zbl1003.42024MR1884234
- J. Ben Hough, Manjunath Krishnapur, Yuval Peres, Bálint Virág, Determinantal processes and independence, Probab. Surv. 3 (2006), 206-229 Zbl1189.60101MR2216966
- 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
- Russell Lyons, Determinantal probability measures, Publ. Math. Inst. Hautes Études Sci. (2003), 167-212 Zbl1055.60003MR2031202
- Saunders Mac Lane, Garrett Birkhoff, Algebra, (1988), Chelsea Publishing Co., New York Zbl0641.12001MR941522

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