A note on gaps in proofs of central limit theorems

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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.

OriginalsprogEngelsk
TidsskriftStatistics & Probability Letters
Vol/bind135
Sider (fra-til)7-10
Antal sider4
ISSN0167-7152
DOI
StatusUdgivet - apr. 2018

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