{"title":"On Sufficient Conditions in the Marchenko--Pastur Theorem","authors":"P. A. Yaskov","doi":"10.1137/s0040585x97t991696","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 68, Issue 4, Page 657-673, February 2024. <br/> 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.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"21 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991696","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
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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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.
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