The generalized symmetric eigenproblem in multivariate statistical models

Abstract

The solution of the generalized symmetric eigenproblem Ax = λBx is required in many multivariate statistical models, viz. canonical correlation, discriminant analysis, multivariate linear model, limited information maximum likelihoods. The problem can be solved by two efficient numerical algorithms: Cholesky decomposition or singular value decomposition. Practical considerations for implementation are also discussed.

Keywords:

• canonical analysis
• statistical computations
• statistical packages
• discriminant analysis
• multivariate linear model
• LIML
• Cholesky
• Householder
• singular value