样本协方差矩阵极值特征值偏差大

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY Journal of Applied Probability Pub Date : 2023-04-24 DOI:10.1017/jpr.2022.130

Denise Uwamariya, Xiangfeng Yang

{"title":"样本协方差矩阵极值特征值偏差大","authors":"Denise Uwamariya, Xiangfeng Yang","doi":"10.1017/jpr.2022.130","DOIUrl":null,"url":null,"abstract":"\n\t Large deviations of the largest and smallest eigenvalues of \n\t \n\t\t\n\t\t\n$\\mathbf{X}\\mathbf{X}^\\top/n$\n\n\t \n\t are studied in this note, where \n\t \n\t\t\n\t\t\n$\\mathbf{X}_{p\\times n}$\n\n\t \n\t is a \n\t \n\t\t\n\t\t\n$p\\times n$\n\n\t \n\t random matrix with independent and identically distributed (i.i.d.) sub-Gaussian entries. The assumption imposed on the dimension size p and the sample size n is \n\t \n\t\t\n\t\t\n$p=p(n)\\rightarrow\\infty$\n\n\t \n\t with \n\t \n\t\t\n\t\t\n$p(n)={\\mathrm{o}}(n)$\n\n\t \n\t . This study generalizes one result obtained in [3].","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Large deviations of extremal eigenvalues of sample covariance matrices\",\"authors\":\"Denise Uwamariya, Xiangfeng Yang\",\"doi\":\"10.1017/jpr.2022.130\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n\\t Large deviations of the largest and smallest eigenvalues of \\n\\t \\n\\t\\t\\n\\t\\t\\n$\\\\mathbf{X}\\\\mathbf{X}^\\\\top/n$\\n\\n\\t \\n\\t are studied in this note, where \\n\\t \\n\\t\\t\\n\\t\\t\\n$\\\\mathbf{X}_{p\\\\times n}$\\n\\n\\t \\n\\t is a \\n\\t \\n\\t\\t\\n\\t\\t\\n$p\\\\times n$\\n\\n\\t \\n\\t random matrix with independent and identically distributed (i.i.d.) sub-Gaussian entries. The assumption imposed on the dimension size p and the sample size n is \\n\\t \\n\\t\\t\\n\\t\\t\\n$p=p(n)\\\\rightarrow\\\\infty$\\n\\n\\t \\n\\t with \\n\\t \\n\\t\\t\\n\\t\\t\\n$p(n)={\\\\mathrm{o}}(n)$\\n\\n\\t \\n\\t . This study generalizes one result obtained in [3].\",\"PeriodicalId\":50256,\"journal\":{\"name\":\"Journal of Applied Probability\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Probability\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/jpr.2022.130\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/jpr.2022.130","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了$\mathbf{X}\mathbf{X}^\top/n$的最大和最小特征值的大偏差，其中$\mathbf{X}_{p\times n}$是一个$p\times n$随机矩阵，具有独立且同分布(i.i.d)的亚高斯条目。对维度大小p和样本量n的假设为$p=p(n)\rightarrow\infty$，其中$p(n)={\mathrm{o}}(n)$。本研究推广了b[3]的一个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Large deviations of extremal eigenvalues of sample covariance matrices

Large deviations of the largest and smallest eigenvalues of

$\mathbf{X}\mathbf{X}^\top/n$

are studied in this note, where

$\mathbf{X}_{p\times n}$

is a

$p\times n$

random matrix with independent and identically distributed (i.i.d.) sub-Gaussian entries. The assumption imposed on the dimension size p and the sample size n is

$p=p(n)\rightarrow\infty$

with

$p(n)={\mathrm{o}}(n)$

. This study generalizes one result obtained in [3].

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.