Moment inequalities for U-statistics

被引：28

作者：

Adamczak, Radoslaw ^{[1
]}

机构：

[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

来源：

ANNALS OF PROBABILITY | 2006年 / 34卷 / 06期

关键词：

U-statistics; concentration of measure;

D O I：

10.1214/009117906000000476

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 present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler norms of the kernel matrix (i.e., norms of some multilinear operators associated with the kernel matrix). As a corollary, we derive tail inequalities for U-statistics with bounded kernels and for some multiple stochastic integrals.

引用

页码：2288 / 2314

页数：27

共 12 条

[1]

Adamczak R., 2005, B POL ACAD SCI MATH, V53, P221, DOI 10.4064/ba53-2-10

[2]

Arcones M. A., 1993, J. Theoret. Probab., V6, P101

[3]

Borell C., 1984, SEMINAR NOTES MULTIP

[4] Moment inequalities for functions of independent random variables [J].

Boucheron, S ;

Bousquet, O ;

Lugosi, G ;

Massart, P .

ANNALS OF PROBABILITY, 2005, 33 (02) :514-560

[5]

DELANPENA VH, 1999, DECOUPLING DEPENDENC

[6] BOUNDS ON THE TAIL PROBABILITY OF U-STATISTICS AND QUADRATIC-FORMS [J].

DELAPENA, VH ;

MONTGOMERYSMITH, SJ .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 31 (02) :223-227

[7] The LIL for canonical U-statistics of order 2 [J].

Giné, E ;

Kwapien, S ;

Latala, R ;

Zinn, J .

ANNALS OF PROBABILITY, 2001, 29 (01) :520-557

[8]

GINE E, 2000, PROGR PROBAB, V47

[9]

Houdré C, 2003, PROG PROBAB, V56, P55

[10]

Kwapien S., 1992, RANDOM SERIES STOCHA

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