论马琴科--帕斯图尔定理中的充分条件

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2024-02-07 DOI:10.1137/s0040585x97t991696

P. A. Yaskov

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引用次数: 0

摘要

概率论及其应用》（Theory of Probability &Its Applications），第 68 卷第 4 期，第 657-673 页，2024 年 2 月。我们为与随机向量相关的高维样本协方差矩阵找到了马琴科--帕斯图尔定理中的一般充分条件，对于这些矩阵，二次形式的弱集中特性可能在一般情况下不成立。这些结果是通过一种新的马氏方法得到的，这种方法可能对随机矩阵理论的其他问题有用。

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On Sufficient Conditions in the Marchenko--Pastur Theorem

Theory of Probability &Its Applications, Volume 68, Issue 4, Page 657-673, February 2024.
We find general sufficient conditions in the Marchenko--Pastur theorem for high-dimensional sample covariance matrices associated with random vectors, for which the weak concentration property of quadratic forms may not hold in general. The results are obtained by means of a new martingale method, which may be useful in other problems of random matrix theory.

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来源期刊

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.