On the central limit theorem for modulus trimmed sums

Alina Bazarova; István Berkes; Lajos Horváth

doi:10.1016/j.spl.2013.12.006

On the central limit theorem for modulus trimmed sums

Alina Bazarova, István Berkes^*, Lajos Horváth

^*Corresponding author for this work

Institute of Statistics (5060)

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

Abstract

We prove a functional central limit theorem for modulus trimmed i.i.d.variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.

Original language	English
Pages (from-to)	61-67
Number of pages	7
Journal	Statistics & Probability Letters
Volume	86
Issue number	1
DOIs	https://doi.org/10.1016/j.spl.2013.12.006 https://doi.org/10.1016/j.spl.2013.12.006
Publication status	Published - Mar 2014

Keywords

Central limit theorem
Iid sums
Modulus trimming
Stable distribution

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Theoretical

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BazarovaBerkesHorvath_CentralLimitTheorem_StatProbLetters_86_61-67_2014.pdfFinal published version, 358 KB

Cite this

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title = "On the central limit theorem for modulus trimmed sums",

abstract = "We prove a functional central limit theorem for modulus trimmed i.i.d.variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.",

keywords = "Central limit theorem, Iid sums, Modulus trimming, Stable distribution",

author = "Alina Bazarova and Istv{\'a}n Berkes and Lajos Horv{\'a}th",

note = "Funding Information: First author{\textquoteright}s research was supported by Austrian Science Fund (FWF) Project W1230. Second author{\textquoteright}s research was supported by Austrian Science Fund (FWF) Grant P24302-N18 and OTKA grant K 108615 . Third author{\textquoteright}s research was supported by NSF grant DMS 1305858 . ",

year = "2014",

month = mar,

doi = "10.1016/j.spl.2013.12.006",

language = "English",

volume = "86",

pages = "61--67",

journal = "Statistics & Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

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T1 - On the central limit theorem for modulus trimmed sums

AU - Bazarova, Alina

AU - Berkes, István

AU - Horváth, Lajos

N1 - Funding Information: First author’s research was supported by Austrian Science Fund (FWF) Project W1230. Second author’s research was supported by Austrian Science Fund (FWF) Grant P24302-N18 and OTKA grant K 108615 . Third author’s research was supported by NSF grant DMS 1305858 .

PY - 2014/3

Y1 - 2014/3

N2 - We prove a functional central limit theorem for modulus trimmed i.i.d.variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.

AB - We prove a functional central limit theorem for modulus trimmed i.i.d.variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.

KW - Central limit theorem

KW - Iid sums

KW - Modulus trimming

KW - Stable distribution

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U2 - 10.1016/j.spl.2013.12.006

DO - 10.1016/j.spl.2013.12.006

M3 - Article

VL - 86

SP - 61

EP - 67

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

IS - 1

ER -

On the central limit theorem for modulus trimmed sums

Abstract

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Asymptotic Probability Theory

Cite this

On the central limit theorem for modulus trimmed sums

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Other files and links

Fingerprint

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Asymptotic Probability Theory

Cite this