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Testing and Estimation for Structures Which Are Circularly Symmetricin Blocks

Olkin, Ingram
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
National Science Foundation (NSF), Models, Structural Analysis, Symmetry


In this report, the circularly symmetric model is extended to the point where the symmetries are exhibited in blocks. In addition, it is shown how maximum likelihood estimators (MLEs) and likelihood ratio tests (LRIs) can be obtained. The circularly symmetric model is reviewed and it is shown how MLEs and LRTs can be obtained by reducing the model to a canonical form. The various ways of generating the extended model (blocked circularity) are discussed. It is noted that a reduction to a canonical form is possible for the block circular case. Hypotheses representing block versions of sphericity, intraclass correlation, circular symmetry, and a general matrix are presented. Also shown are likelihood ratio tests and their approximate null distribution for testing symmetric structures and tests for means given that the covariance matrix is circular. (JS) (21pp.)

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