Applications of the Frobenius norm criterion in multivariate analysi

In several multivariate problems, the test statistics are based on the determinant, the trace, or the largest eigenvalue of some positive definite matrix. However, these matrix operators have their drawbacks. Hence, alternative functions of matrices need to be considered. This dissertation considers various asymptotic multivariate tests based on the Frobenius norm criterion. This criterion shall be used as (1) a criterion for selecting the best subset of predictor variables in multivariate multiple linear regression, (2) an asymptotic method for testing factor effects and the equality of several population variance-covariance matrices in multivariate analysis of variance, (3) an asymptotic method of developing a multivariate control chart for the factor effects and variance-covariance matrix, (4) an optimal criterion for selecting principal components, and (5) an asymptotic method of testing the independence of two sets of variables in canonical correlation analysis.