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

本研究将寻求多元正则变分的结果及其应用。应用将是最小二乘估计与随机预测的多元回归。值得注意的是，对潜在分布的假设将是最小的，允许无限的时刻和分布类型之间的差异。研究的基本问题是随机向量与独立标量的乘积和由随机向量形成的叉积矩阵的概率尾的规则变化。要研究的一个相关问题将涉及到卷积的指数尾行为。将寻求次指数性和卷积等价概念的扩展。本研究将对复合多元分布的多元无穷可分律有一定的应用价值。

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.