Mathematical Sciences: Multivariable Regular and ExponentialVariation with Application to Multiple Regression and to Convolutions of Multivariate Distributions

数学科学：多变量正则和指数变分及其在多元回归和多元分布卷积中的应用

• 批准号: 8711924
• 负责人: Daren Cline
• 金额: $ 2.59万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1990-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8711924&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multivariable; Regular; ExponentialVariation

This research will seek results and their applications of multivariate regular variation. The applications will be to least square estimators in multiple regression with random predictors. The notable part will be that the assumptions on the underlying distributions will be minimal, allowing for infinite moments and disparity among distributional types. Basic among problems of study is the regular variation of probability tails for product of a random vector with an independent scaler and for the matrix of cross products formed from a random vector. A related problem to be studied will involve the exponential tail behavior of convolutions. Extensions of the concepts of subexponentiality and convolution equivalency will be sought. The research will have applications for multivariate infinitely divisible laws for compound multivariate distributions.

这项研究将寻求结果及其应用， 多元正则变分 这些应用程序将用于 随机变量多元回归中最小二乘估计 预测器 值得注意的是， 潜在的分布将是最小的，允许无限的 分布类型间的矩和差异。 基本在 研究的问题是概率尾的规律性变化 对于随机向量与独立定标器的乘积， 由随机向量形成的叉积矩阵。 一 相关的问题要研究将涉及指数尾部 卷积的行为。 概念的扩展 将寻求次指数性和卷积等价性。 该研究将在多变量无穷 复合多元分布的可除律