ScholarLens Back to search
1980•Journal of the American Statistical AssociationRequires access

Product Inequalities Involving the Multivariate Normal Distribution

R. L. Dykstra

Open publisher page 4 citations

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.

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available 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.

Key concepts: Matrix t-distribution, Normal-Wishart distribution, Mathematics, Multivariate statistics, Multivariate normal distribution, Wishart distribution, Multivariate t-distribution, Matrix normal distribution

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Product Inequalities Involving the Multivariate Normal Distribution — Research Paper | ScholarLens