A note on gaps in proofs of central limit theorems

By Christophe A.N. Biscio, Arnaud Poinas and Rasmus Waagepetersen
CSGB Research Reports
No. 12, November 2017

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.

Keywords: Central limit theorem, Cramér-Wold device, random field.

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