A note on gaps in proofs of central limit theorems

Christophe Ange Napoléon Biscio, Arnaud Poinas and Rasmus Waagepetersen

Statistics & Probability Letters, 2018, vol. 135, issue C, 7-10

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.

Keywords: Central limit theorem; Cramér–Wold device; Random field (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2017.11.009

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