Tests of Linear Hypotheses

  • R. B. Bapat
Part of the Universitext book series (UTX)


Basic properties of the multivariate normal distribution are proved. The independence of quadratic forms and the independence of a quadratic form and a linear form in a multivariate normal are characterized. The matrix version of the Cochran’s Theorem is formulated with a succinct proof. The results are applied to the one-way and two-way classification, with and without interaction. The general linear hypothesis is considered and the corresponding F-test is developed. Maximum likelihood estimates of the parameters in a linear model are obtained. The multiple correlation coefficient is defined and its relation with the F-statistic for the significance of the regression coefficients is proved.


Quadratic Form Conditional Distribution Positive Semidefinite Maximum Correlation Multivariate Normal Distribution 
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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • R. B. Bapat
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

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