A note on gaps in proofs of central limit theorems

作者：Biscio Christophe Ange Napoleon^*; Poinas Arnaud; Waagepetersen Rasmus

来源：Statistics & Probability Letters, 2018, 135: 7-10.

DOI：10.1016/j.sp1.2017.11.009

• Central limit theorem
• Cramer-Wold device
• Random field

We fill two gaps in the literature on central limit theorems. First we state and prove a generalization of the Cramer-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.

• 出版日期2018-4