Remarks on Multivariate Confidence Bounds.

Abstract

Confidence bounds are given for all bilinear forms a'(theta)b in the parameters of the multivariate linear model using any phi belonging to the class Phi of functions increasing in the eigenvalues of a random matrix. An extension yields simultaneous tests for all hypotheses H: A'(Theta)B = 0 using any phi epsilon Phi. The optimality of the Roy-Bose bounds for a'(theta)b in the class Phi is established. These findings are consequences of a variational lemma which yields bounds on the joint distribution of Friedman's statistics even in small samples. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 15, 1973
Accession Number
AD0763463

Entities

People

  • Donald R. Jensen

Organizations

  • Virginia Tech

Tags

DTIC Thesaurus Topics

  • Computing-Related Activities
  • Data Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Hypotheses
  • Information Science
  • Mathematics
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.