A note on gaps in proofs of central limit theorems

Christophe Biscio; Arnaud  Poinas; Rasmus Plenge Waagepetersen

doi:10.1016/j.spl.2017.11.009

A note on gaps in proofs of central limit theorems

Christophe Biscio, Arnaud Poinas, Rasmus Plenge Waagepetersen

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

4 Citationer (Scopus)

Abstrakt

We fill two gaps in the literature on central limit theorems. First we state and prove a generalization of the Cramér–Wold device which is useful for establishing multivariate central limit theorems without the need for assuming the existence of a limiting covariance matrix. Second we extend and provide a detailed proof of a very useful result for establishing univariate central limit theorems.

Originalsprog	Engelsk
Tidsskrift	Statistics & Probability Letters
Vol/bind	135
Sider (fra-til)	7-10
Antal sider	4
ISSN	0167-7152
DOI	https://doi.org/10.1016/j.spl.2017.11.009
Status	Udgivet - apr. 2018

Adgang til dokumentet

10.1016/j.spl.2017.11.009

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Citationsformater

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abstract = "We fill two gaps in the literature on central limit theorems. First we state and prove a generalization of the Cram{\'e}r–Wold device which is useful for establishing multivariate central limit theorems without the need for assuming the existence of a limiting covariance matrix. Second we extend and provide a detailed proof of a very useful result for establishing univariate central limit theorems.",

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AU - Biscio, Christophe

AU - Poinas, Arnaud

AU - Waagepetersen, Rasmus Plenge

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N2 - We fill two gaps in the literature on central limit theorems. First we state and prove a generalization of the Cramér–Wold device which is useful for establishing multivariate central limit theorems without the need for assuming the existence of a limiting covariance matrix. Second we extend and provide a detailed proof of a very useful result for establishing univariate central limit theorems.

AB - We fill two gaps in the literature on central limit theorems. First we state and prove a generalization of the Cramér–Wold device which is useful for establishing multivariate central limit theorems without the need for assuming the existence of a limiting covariance matrix. Second we extend and provide a detailed proof of a very useful result for establishing univariate central limit theorems.

U2 - 10.1016/j.spl.2017.11.009

DO - 10.1016/j.spl.2017.11.009

M3 - Journal article

VL - 135

SP - 7

EP - 10

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

ER -