Estimation of the density of a determinantal process
Baraud, Yannick
Confluentes Mathematici, Tome 5 (2013), p. 3-21 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 2013-01-01
DOI : https://doi.org/10.5802/cml.1
Classification:  62G07,  62M30 
@article{CML_2013__5_1_3_0,
     author = {Baraud, Yannick},
     title = {Estimation of the density of a determinantal process},
     journal = {Confluentes Mathematici},
     volume = {5},
     year = {2013},
     pages = {3-21},
     doi = {10.5802/cml.1},
     mrnumber = {3143610},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CML_2013__5_1_3_0}
}

Baraud, Yannick. Estimation of the density of a determinantal process. Confluentes Mathematici, Tome 5 (2013) pp. 3-21. doi : 10.5802/cml.1. http://gdmltest.u-ga.fr/item/CML_2013__5_1_3_0/

[1] Akakpo, N. Estimation adaptative par selection de partitions en rectangles dyadiques, University Paris XI (2009) (Ph. D. Thesis)

[2] Anderson, Greg W.; Guionnet, Alice; Zeitouni, Ofer An introduction to random matrices, Cambridge University Press, Cambridge, Cambridge Studies in Advanced Mathematics, Tome 118 (2010) | MR 2760897 | Zbl 1184.15023

[3] Baik, Jinho; Rains, Eric M. Algebraic aspects of increasing subsequences, Duke Math. J., Tome 109 (2001) no. 1, pp. 1-65 | Article | MR 1844203 | Zbl 1007.05096

[4] Baraud, Yannick Estimator selection with respect to Hellinger-type risks, Probab. Theory Related Fields, Tome 151 (2011) no. 1-2, pp. 353-401 | Article | MR 2834722 | Zbl pre05968717

[5] Birgé, Lucien Model selection via testing: an alternative to (penalized) maximum likelihood estimators, Ann. Inst. H. Poincaré Probab. Statist., Tome 42 (2006) no. 3, pp. 273-325 | Article | Numdam | MR 2219712 | Zbl pre05024238

[6] Borodin, Alexei; Diaconis, Persi; Fulman, Jason On adding a list of numbers (and other one-dependent determinantal processes), Bull. Amer. Math. Soc. (N.S.), Tome 47 (2010) no. 4, pp. 639-670 | Article | MR 2721041 | Zbl 1230.05292

[7] De Bruijn, N. G. On some multiple integrals involving determinants, J. Indian Math. Soc. (N.S.), Tome 19 (1955), p. 133-151 (1956) | MR 79647 | Zbl 0068.24904

[8] Hochmuth, Reinhard Wavelet characterizations for anisotropic Besov spaces, Appl. Comput. Harmon. Anal., Tome 12 (2002) no. 2, pp. 179-208 | Article | MR 1884234 | Zbl 1003.42024

[9] Hough, J. Ben; Krishnapur, Manjunath; Peres, Yuval; Virág, Bálint Determinantal processes and independence, Probab. Surv., Tome 3 (2006), pp. 206-229 | Article | MR 2216966 | Zbl 1189.60101

[10] Hough, J. Ben; Krishnapur, Manjunath; Peres, Yuval; Virág, Bálint Zeros of Gaussian analytic functions and determinantal point processes, American Mathematical Society, Providence, RI, University Lecture Series, Tome 51 (2009) | MR 2552864 | Zbl 1190.60038

[11] Lyons, Russell Determinantal probability measures, Publ. Math. Inst. Hautes Études Sci. (2003) no. 98, pp. 167-212 | Article | Numdam | MR 2031202 | Zbl 1055.60003

[12] Mac Lane, Saunders; Birkhoff, Garrett Algebra, Chelsea Publishing Co., New York (1988) | MR 941522 | Zbl 0641.12001