对部分广义四矩定理的再认识

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-11-01 DOI:10.3150/20-BEJ1310

Dandan Jiang, Z. Bai

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引用次数: 3

摘要

这是“广义四矩定理（G4MT）及其在高维协方差矩阵尖峰特征值CLT中的应用”中提到和描述的部分广义4矩定理（PG4MT）的补充证明。由于该文提出的G4MT要求矩阵X和Y都满足假设maxt，s|uts|2E{|x11|4I（|x11|＜n）-μ}→0，这在实际应用中可能是限制性的，我们提出了一种新的G4MT，称为PG4MT，没有证据。在ArXiv提出手稿后，作者通过私人通信对PG4MT的证明产生了高度兴趣，并发现PG4MT比G4MT更通用，有必要对其进行详细的证明。此外，发现PG4MT导出了样本协方差矩阵的尖峰特征值的CLT，该CLT涵盖了Bai和Yao（J.Multivariate Anal.106（2012）167–177）作为特例的工作。

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Partial generalized four moment theorem revisited

This is a complementary proof of partial generalized 4 moment theorem (PG4MT) mentioned and described in “Generalized Four Moment Theorem (G4MT) and its Application to CLT for Spiked Eigenvalues of High-dimensional Covariance Matrices”. Since the G4MT proposed in that paper requires both the matrices X and Y satisfying the assumption maxt,s|uts|2E{|x11|4I(|x11|

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.

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