Admissibility of some tests, multiple decision procedures and classification procedures in multivariate analysis (Q1310536)

The Bayesian method is used to derive the admissibility of various procedures. In Section 3, two testing problems related to a given structure of means and the sphericity covariance structure are treated. The admissibility of the likelihood ratio test is shown for each problem. Testing problems for covariance matrices are studied in Section 4. One- sided tests for one- and two-sample cases are studied. The linear structure for the inverse matrix of a covariance matrix is also considered. A class of admissible tests is obtained for each problem. In Section 5, multiple decision problems for covariance matrices are dealt with in two- and three-samples cases. A class of admissible procedures are obtained for each problem. In Section 6, the classification problem with unequal covariance matrices is studied. Three rules which have the same limiting distribution are derived. It is shown that two of them are admissible. Numerical simulations are carried out to examine some properties of the three rules.