Distributions of Characteristic Roots in Multivariate Analysis
Abstract
A review of the work on distributions of characteristic (ch.) roots in real Gaussian multivariate analysis has been attempted surveying the developments in the field from the start covering about fifty years. The exact null and non-null distributions of the ch. roots have been reviewed and sub- asymptotic and asymptotic expansions of the distributions mostly for large sample sizes studied by various authors, have been briefly discussed. Such distributional studies of four test criteria and a few less important ones which are functions of ch. roots have further been discussed in view of the power comparison made in connection with tests of three multivariate hypotheses. In addition, one-sample case has also been considered in terms of distributional aspects of the ch. roots and criteria for tests of two hypotheses on the covariance matrix. A brief critical review has also been attempted. For convenience in organization, the review has been given in two parts: Part I. Null distributions and Part II. Non-null distributions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1976
- Accession Number
- ADA030867
Entities
People
- K. C. Pillai
Organizations
- Purdue University