On moments of truncated multivariate normal/independent distributions

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY Journal of Multivariate Analysis Pub Date : 2023-11-02 DOI:10.1016/j.jmva.2023.105248

Tsung-I Lin , Wan-Lun Wang

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Abstract

Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate $t$ , 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.

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关于截断多元正态/独立分布的矩

多变量正态/独立(MNI)分布包含许多著名的重尾分布，如多变量t分布、多变量斜线分布、多变量污染正态分布、多变量方差-伽马分布和多变量双指数分布。统计分析中经常遇到的一个问题是出现截断观测值和非正态性，因此需要理论矩来估计截断多元正态/独立(TMNI)分布。本文致力于推导出在超矩形内支承的TMNI分布的矩的显式表达式。通过蒙特卡罗实验，对五个选定的TMNI分布进行了验证。在GitHub存储库中可以获得用于复制结果的R脚本和数据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Multivariate Analysis 数学-统计学与概率论

CiteScore

2.40

自引率

25.00%

发文量

108

审稿时长

74 days

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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