Almost sure limit theorems for U-statistics

Hajo Holzmann; Susanne Koch; Aleksey Min

doi:10.1016/j.spl.2004.06.019

Almost sure limit theorems for U-statistics

Hajo Holzmann
, Susanne Koch
, Aleksey Min

Georg August Universität Göttingen

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

9 Scopus citations

Abstract

We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki [(Stochastic Process. Appl. 94 (2001) 105)]. We extend this result to the case of convergence to stable laws and also prove a functional version.

Original language	English
Pages (from-to)	261-269
Number of pages	9
Journal	Statistics and Probability Letters
Volume	69
Issue number	3
DOIs	https://doi.org/10.1016/j.spl.2004.06.019
State	Published - 15 Sep 2004
Externally published	Yes

Keywords

Almost sure limit theorem
Functional limit theorem
Stable distributions
U-statistics

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10.1016/j.spl.2004.06.019

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title = "Almost sure limit theorems for U-statistics",

abstract = "We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki [(Stochastic Process. Appl. 94 (2001) 105)]. We extend this result to the case of convergence to stable laws and also prove a functional version.",

keywords = "Almost sure limit theorem, Functional limit theorem, Stable distributions, U-statistics",

author = "Hajo Holzmann and Susanne Koch and Aleksey Min",

year = "2004",

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doi = "10.1016/j.spl.2004.06.019",

language = "English",

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T1 - Almost sure limit theorems for U-statistics

AU - Holzmann, Hajo

AU - Koch, Susanne

AU - Min, Aleksey

PY - 2004/9/15

Y1 - 2004/9/15

N2 - We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki [(Stochastic Process. Appl. 94 (2001) 105)]. We extend this result to the case of convergence to stable laws and also prove a functional version.

AB - We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki [(Stochastic Process. Appl. 94 (2001) 105)]. We extend this result to the case of convergence to stable laws and also prove a functional version.

KW - Almost sure limit theorem

KW - Functional limit theorem

KW - Stable distributions

KW - U-statistics

UR - https://www.scopus.com/pages/publications/4444307874

U2 - 10.1016/j.spl.2004.06.019

DO - 10.1016/j.spl.2004.06.019

M3 - Article

AN - SCOPUS:4444307874

SN - 0167-7152

VL - 69

SP - 261

EP - 269

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

Almost sure limit theorems for U-statistics

Abstract

Keywords

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