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

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Statistik (5060)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Seiten (von - bis)	61-67
Seitenumfang	7
Fachzeitschrift	Statistics & Probability Letters
Jahrgang	86
Ausgabenummer	1
DOIs	https://doi.org/10.1016/j.spl.2013.12.006
Publikationsstatus	Veröffentlicht - März 2014

ASJC Scopus subject areas

Statistik und Wahrscheinlichkeit
Statistik, Wahrscheinlichkeit und Ungewissheit

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Theoretical

Zugriff auf Dokument

10.1016/j.spl.2013.12.006

on_the_central_limit_theorem_for_modules_trimmed_sumsAkzeptiertes Autorenmanuskript, 95,3 KBLizenz: CC BY 4.0
BazarovaBerkesHorvath_CentralLimitTheorem_StatProbLetters_86_61-67_2014.pdfEndgültige, publizierte Fassung, 358 KB

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Verknüpfung zur Publikation in Scopus

Asymptotische Wahrscheinlichkeitstheorie
Schauer, J., Hörmann, S. & Berkes, I.
1/01/03 → …
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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 . ",

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

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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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DO - 10.1016/j.spl.2013.12.006

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JO - Statistics & Probability Letters

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On the central limit theorem for modulus trimmed sums

Abstract

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Zugriff auf Dokument

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Projekte

Asymptotische Wahrscheinlichkeitstheorie

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