Geodesic
Concentration inequalities for smooth random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 401-410 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some deterministic point plus an intrinsic dimension of the optimization problem. As an application we prove the exponential inequality for a function of the maximal eigenvalue of a random matrix.
Keywords: smooth random fields; concentration inequalities; maximal eigenvalue of a random matrix. 
@article{TVP_2013_58_2_a12,
     author = {D. V. Belomestny and V. G. Spokoiny},
     title = {Concentration inequalities for smooth random fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {401--410},
     year = {2013},
     volume = {58},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a12/}
}
TY  - JOUR
AU  - D. V. Belomestny
AU  - V. G. Spokoiny
TI  - Concentration inequalities for smooth random fields
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2013
SP  - 401
EP  - 410
VL  - 58
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a12/
LA  - en
ID  - TVP_2013_58_2_a12
ER  - 
%0 Journal Article
%A D. V. Belomestny
%A V. G. Spokoiny
%T Concentration inequalities for smooth random fields
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2013
%P 401-410
%V 58
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a12/
%G en
%F TVP_2013_58_2_a12
D. V. Belomestny; V. G. Spokoiny. Concentration inequalities for smooth random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 401-410. http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a12/

[1] Bednorz W., “A theorem on majorizing measures”, Ann. Probab., 34:5 (2006), 1771–1781 | DOI | MR | Zbl

[2] Ledoux M., The Concentration of Measure Phenomenon, Amer. Math. Soc., Providence, RI, 2001, 181 pp. | MR | Zbl

[3] Lugosi G., Concentration-of-Measure Inequalities: Lecture Notes, , 2005 http://www.econ.upf.edu/l̃ugosi/anu.pdf

[4] Mackey L., Jordan M. I., Chen R. Y., Farrell B., Tropp J. A., Matrix concentration inequalities via the method of exchangeable pairs, arXiv: 1201.6002

[5] Massart P., “Some applications of concentration inequalities to statistics”, Ann. Fac. Sci. Toulouse, 9:2 (2000), 245–303 | DOI | MR | Zbl

[6] Spokoiny V., Parametric estimation. Finite sample theory, arXiv: 1111.3029v4 | MR

[7] Talagrand M., The Generic Chaining, Springer-Verlag, Berlin, 2005, 222 pp. | MR | Zbl