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A note on gaps in proofs of central limit theorems

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  • Biscio, Christophe Ange Napoléon
  • Poinas, Arnaud
  • Waagepetersen, Rasmus

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.

Suggested Citation

  • Biscio, Christophe Ange Napoléon & Poinas, Arnaud & Waagepetersen, Rasmus, 2018. "A note on gaps in proofs of central limit theorems," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 7-10.
    • Handle: RePEc:eee:stapro:v:135:y:2018:i:c:p:7-10
    DOI: 10.1016/j.spl.2017.11.009
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    References listed on IDEAS

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    1. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
    2. Guan, Yongtao & Loh, Ji Meng, 2007. "A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1377-1386, December.
    3. Rasmus Plenge Waagepetersen, 2007. "An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes," Biometrics, The International Biometric Society, vol. 63(1), pages 252-258, March.
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    Cited by:

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