A Note on Distribution-Free Symmetrization Inequalities

Zhao Dong; Jiange Li; Wenbo V. Li

doi:10.1007/s10959-014-0538-z

A Note on Distribution-Free Symmetrization Inequalities

Zhao Dong
, Jiange Li^*
, Wenbo V. Li

^*Corresponding author for this work

CAS - Institute of Applied Mathematics
University of Delaware

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

7 Scopus citations

Abstract

Let X, YX, Y be two independent identically distributed (i.i.d.) random variables taking values from a separable Banach space [InlineEquation not available: see fulltext.]. Given two measurable subsets [InlineEquation not available: see fulltext.], we establish distribution-free comparison inequalities between (Formula presented.) and (Formula presented.). These estimates are optimal for real random variables as well as when [InlineEquation not available: see fulltext.] is equipped with the (Formula presented.) norm. Our approach for both problems extends techniques developed by Schultze and Weizsächer (Adv Math 208:672–679, 2007).

Original language	English
Pages (from-to)	958-967
Number of pages	10
Journal	Journal of Theoretical Probability
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s10959-014-0538-z
State	Published - 1 Sep 2015
Externally published	Yes

Keywords

Covering number
Distribution-free
Kissing number
Symmetrization inequalities

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10.1007/s10959-014-0538-z

Cite this

@article{2f8f18a52a1c407f8dcdafbfc9add388,

title = "A Note on Distribution-Free Symmetrization Inequalities",

abstract = "Let X, YX, Y be two independent identically distributed (i.i.d.) random variables taking values from a separable Banach space [InlineEquation not available: see fulltext.]. Given two measurable subsets [InlineEquation not available: see fulltext.], we establish distribution-free comparison inequalities between (Formula presented.) and (Formula presented.). These estimates are optimal for real random variables as well as when [InlineEquation not available: see fulltext.] is equipped with the (Formula presented.) norm. Our approach for both problems extends techniques developed by Schultze and Weizs{\"a}cher (Adv Math 208:672–679, 2007).",

keywords = "Covering number, Distribution-free, Kissing number, Symmetrization inequalities",

author = "Zhao Dong and Jiange Li and Li, \{Wenbo V.\}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2015",

month = sep,

day = "1",

doi = "10.1007/s10959-014-0538-z",

language = "英语",

volume = "28",

pages = "958--967",

journal = "Journal of Theoretical Probability",

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TY - JOUR

T1 - A Note on Distribution-Free Symmetrization Inequalities

AU - Dong, Zhao

AU - Li, Jiange

AU - Li, Wenbo V.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - Let X, YX, Y be two independent identically distributed (i.i.d.) random variables taking values from a separable Banach space [InlineEquation not available: see fulltext.]. Given two measurable subsets [InlineEquation not available: see fulltext.], we establish distribution-free comparison inequalities between (Formula presented.) and (Formula presented.). These estimates are optimal for real random variables as well as when [InlineEquation not available: see fulltext.] is equipped with the (Formula presented.) norm. Our approach for both problems extends techniques developed by Schultze and Weizsächer (Adv Math 208:672–679, 2007).

AB - Let X, YX, Y be two independent identically distributed (i.i.d.) random variables taking values from a separable Banach space [InlineEquation not available: see fulltext.]. Given two measurable subsets [InlineEquation not available: see fulltext.], we establish distribution-free comparison inequalities between (Formula presented.) and (Formula presented.). These estimates are optimal for real random variables as well as when [InlineEquation not available: see fulltext.] is equipped with the (Formula presented.) norm. Our approach for both problems extends techniques developed by Schultze and Weizsächer (Adv Math 208:672–679, 2007).

KW - Covering number

KW - Distribution-free

KW - Kissing number

KW - Symmetrization inequalities

UR - https://www.scopus.com/pages/publications/84945454517

U2 - 10.1007/s10959-014-0538-z

DO - 10.1007/s10959-014-0538-z

M3 - 文章

AN - SCOPUS:84945454517

SN - 0894-9840

VL - 28

SP - 958

EP - 967

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 3

ER -

A Note on Distribution-Free Symmetrization Inequalities

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Keywords

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