{"title":"Power Enhancement for Dimension Detection of Gaussian Signals","authors":"Gaspard Bernard, Thomas Verdebout","doi":"10.5705/ss.202022.0315","DOIUrl":null,"url":null,"abstract":"In the present section, our objective is to provide Monte-Carlo simulation results to corroborate the conclusions drawn from Proposition 1 and in Section 4. In the first simulation exercise, the objective is to illustrate Proposition 1. We generated M = 10, 000 independent samples of i.i.d. observations X (b) 1 , . . . ,X (b) 10,000, for b = 0, 1 4 , 1 2 , 1. The X (b) i ’s are i.i.d. with a common (p = 8)-dimensional Gaussian distribution with mean zero and covariance matrix","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5705/ss.202022.0315","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In the present section, our objective is to provide Monte-Carlo simulation results to corroborate the conclusions drawn from Proposition 1 and in Section 4. In the first simulation exercise, the objective is to illustrate Proposition 1. We generated M = 10, 000 independent samples of i.i.d. observations X (b) 1 , . . . ,X (b) 10,000, for b = 0, 1 4 , 1 2 , 1. The X (b) i ’s are i.i.d. with a common (p = 8)-dimensional Gaussian distribution with mean zero and covariance matrix
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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