Estimation and Tests for Unknown Linear Restriction in Multivariate Linear Models.

Abstract

This report considers the multivariate linear regression model X = F1 Xi F2 +E, where X is a c x N matrix of observations, F1 is a known c x p matrix of covariates, F2 is a known m x N design matrix (containing values of independent variables in the regression), and XI is an unknown p x m matrix of regression coefficients assumed under a null hypothesis H0 to satisfy a system of linear restraints of the form H0: U1 Xi F3 = ab, where F3: m x k and b: s x h are known matrices, and U1: r x p and alpha: r x s (s < or = r < or = p) are unknown matrices of restraint coefficients. The error matrix E: c x N is assumed to have columns which are statistically independent, multivariate normal random vectors with common mean vector 0 and common unknown matrix sigma.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1976
Accession Number
ADA037530

Entities

People

  • John Douglas Healy

Organizations

  • Purdue University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Analysis Of Variance
  • Coefficients
  • Consistency
  • Covariance
  • Data Science
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Estimators
  • Experimental Design
  • Information Science
  • Normal Distribution
  • Probability
  • Random Variables
  • Square Roots
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Regression Analysis.