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ERIC Number: ED069729
Record Type: RIE
Publication Date: 1972-Aug
Pages: 21
Abstractor: N/A
Testing and Estimation for Structures which are Circularly Symmetric in Blocks.
Olkin, Ingram
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 (LRTs) 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)
Publication Type: N/A
Education Level: N/A
Audience: N/A
Language: N/A
Sponsor: National Science Foundation, Washington, DC.
Authoring Institution: Educational Testing Service, Princeton, NJ.
Note: Draft