On concentration inequalities for vector-valued Lipschitz functions

被引：0

作者：

Katselis, Dimitrios ^{[1
]}

Xie, Xiaotian ^{[2
,3
]}

Beck, Carolyn L. ^{[2
,3
]}

Srikant, R. ^{[1
,3
]}

机构：

[1] Univ Illinois, ECE Dept, Champaign, IL 61820 USA

[2] Univ Illinois, ISE Dept, Champaign, IL USA

[3] Univ Illinois, Coordinated Sci Lab, Champaign, IL USA

来源：

STATISTICS & PROBABILITY LETTERS | 2021年 / 173卷

关键词：

Theorem of Bobkov and Gotze; Concentration; Markov chain; Transportation cost inequality;

D O I：

10.1016/j.spl.2021.109071

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct application of a classical theorem due to Bobkov and Gotze. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：6

共 50 条

[1] BANACH SPACES OF LIPSCHITZ FUNCTIONS AND VECTOR-VALUED LIPSCHITZ FUNCTIONS
JOHNSON, JA
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 148 (01) : 147 - &
[2] BANACH SPACES OF LIPSCHITZ FUNCTIONS AND VECTOR-VALUED LIPSCHITZ FUNCTIONS
JOHNSON, JA
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 75 (06) : 1334 - &
[3] On the structure of spaces of vector-valued Lipschitz functions
Garcia-Lirola, Luis
Petitjean, Colin
Zoca, Abraham Rueda
[J]. STUDIA MATHEMATICA, 2017, 239 (03) : 249 - 271
[4] VARIATIONAL INEQUALITIES FOR VECTOR-VALUED FUNCTIONS
HILDEBRANDT, S
WIDMAN, KO
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1979, 309 : 191 - 220
[5] ON LOCALLY LIPSCHITZ VECTOR-VALUED INVEX FUNCTIONS
YEN, ND
SACH, PH
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1993, 47 (02) : 259 - 272
[6] On the action of Lipschitz functions on vector-valued random sums
Van Neerven J.
Veraar M.
[J]. Archiv der Mathematik, 2005, 85 (6) : 544 - 553
[7] ON GENERALIZED DIFFERENTIALS AND SUBDIFFERENTIALS OF LIPSCHITZ VECTOR-VALUED FUNCTIONS
THIBAULT, L
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (10) : 1037 - 1053
[8] On the action of Lipschitz functions on vector-valued random sums
van Neerven, J
Veraar, M
[J]. ARCHIV DER MATHEMATIK, 2005, 85 (06) : 544 - 553
[9] The Daugavet property in spaces of vector-valued Lipschitz functions
Zoca, Abraham Rueda
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (02)
[10] Characterization of quasiconvexity for locally Lipschitz vector-valued functions
Benoist, J
[J]. OPTIMIZATION, 2003, 52 (02) : 145 - 152

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