{"title":"关于截断多元正态/独立分布的矩","authors":"Tsung-I Lin , Wan-Lun Wang","doi":"10.1016/j.jmva.2023.105248","DOIUrl":null,"url":null,"abstract":"<div><p>Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate <span><math><mi>t</mi></math></span>, multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. <span>R</span> scripts and data to reproduce the results are available in the GitHub repository.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"199 ","pages":"Article 105248"},"PeriodicalIF":1.4000,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23000945/pdfft?md5=3cb17094e738a982bd8a526ea82d616f&pid=1-s2.0-S0047259X23000945-main.pdf","citationCount":"0","resultStr":"{\"title\":\"On moments of truncated multivariate normal/independent distributions\",\"authors\":\"Tsung-I Lin , Wan-Lun Wang\",\"doi\":\"10.1016/j.jmva.2023.105248\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate <span><math><mi>t</mi></math></span>, multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. <span>R</span> scripts and data to reproduce the results are available in the GitHub repository.</p></div>\",\"PeriodicalId\":16431,\"journal\":{\"name\":\"Journal of Multivariate Analysis\",\"volume\":\"199 \",\"pages\":\"Article 105248\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0047259X23000945/pdfft?md5=3cb17094e738a982bd8a526ea82d616f&pid=1-s2.0-S0047259X23000945-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Multivariate Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0047259X23000945\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X23000945","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
On moments of truncated multivariate normal/independent distributions
Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate , multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. R scripts and data to reproduce the results are available in the GitHub repository.
期刊介绍：
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.
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