Product Inequalities Involving the Multivariate Normal Distribution
研究了多元正态随机向量在凸对称区域上的乘积不等式，给出了条件使得这些不等式成立，并应用于多元回归中保守的同时置信区域。
Abstract Suppose Y′ = (Y′ 1, …, Y′ k ) possesses a multivariate normal distribution with mean vector 0 and positive semidefinite covariance matrix Σ. If Ci ⊂ Rpi denote convex regions symmetric about the origin, then conditions are given such that and/or obtain. These conditions imply that chi-squared random variables defined from a multivariate normal distribution are always positively dependent and nonnegatively correlated. Other applications involve conservative simultaneous confidence regions in a multivariate regression setting.