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

Research output: Contribution to journal › Journal article › Research › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Statistics & Probability Letters
Volume	135
Pages (from-to)	7-10
Number of pages	4
ISSN	0167-7152
DOIs	https://doi.org/10.1016/j.spl.2017.11.009
Publication status	Published - Apr 2018

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title = "A note on gaps in proofs of central limit theorems",

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.",

author = "Christophe Biscio and Arnaud Poinas and Waagepetersen, {Rasmus Plenge}",

year = "2018",

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T1 - A note on gaps in proofs of central limit theorems

AU - Biscio, Christophe

AU - Poinas, Arnaud

AU - Waagepetersen, Rasmus Plenge

PY - 2018/4

Y1 - 2018/4

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

SN - 0167-7152

VL - 135

SP - 7

EP - 10

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

ER -

A note on gaps in proofs of central limit theorems

Abstract

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