Concentration of empirical distribution functions with applications to non-i.i.d. models

S. G. Bobkov; F. Götze

doi:10.3150/10-BEJ254

Concentration of empirical distribution functions with applications to non-i.i.d. models

S. G. Bobkov, F. Götze

School of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincaré-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical distribution functions associated with high-dimensional random matrices.

Original language	English (US)
Pages (from-to)	1385-1414
Number of pages	30
Journal	Bernoulli
Volume	16
Issue number	4
DOIs	https://doi.org/10.3150/10-BEJ254
State	Published - Nov 2010

Keywords

Empirical measures
Logarithmic Sobolev inequalities
Poincaré-type inequalities
Random matrices
Spectral distributions

Publisher link

10.3150/10-BEJ254

Find It

Find It at U of M Libraries

Cite this

@article{0abf330de5924ccc930c033f913e9529,

title = "Concentration of empirical distribution functions with applications to non-i.i.d. models",

abstract = "The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar{\'e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical distribution functions associated with high-dimensional random matrices.",

keywords = "Empirical measures, Logarithmic Sobolev inequalities, Poincar{\'e}-type inequalities, Random matrices, Spectral distributions",

author = "Bobkov, {S. G.} and F. G{\"o}tze",

year = "2010",

month = nov,

doi = "10.3150/10-BEJ254",

language = "English (US)",

volume = "16",

pages = "1385--1414",

journal = "Bernoulli",

issn = "1350-7265",

publisher = "International Statistical Institute",

number = "4",

}

TY - JOUR

T1 - Concentration of empirical distribution functions with applications to non-i.i.d. models

AU - Bobkov, S. G.

AU - Götze, F.

PY - 2010/11

Y1 - 2010/11

N2 - The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincaré-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical distribution functions associated with high-dimensional random matrices.

AB - The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincaré-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical distribution functions associated with high-dimensional random matrices.

KW - Empirical measures

KW - Logarithmic Sobolev inequalities

KW - Poincaré-type inequalities

KW - Random matrices

KW - Spectral distributions

UR - http://www.scopus.com/inward/record.url?scp=79251555293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79251555293&partnerID=8YFLogxK

U2 - 10.3150/10-BEJ254

DO - 10.3150/10-BEJ254

M3 - Article

AN - SCOPUS:79251555293

SN - 1350-7265

VL - 16

SP - 1385

EP - 1414

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Concentration of empirical distribution functions with applications to non-i.i.d. models

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this