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Relative Efficiencies of Estimates Using Patterned Covariances or Correlations in the Multivariate Normal Estimation Problem NSF ANCOVA

Author(s):
Szatrowski, Ted H.
Publication Year:
1981
Report Number:
RR-81-37, PSRTR-81-15
Source:
ETS Research Report
Document Type:
Report
Page Count:
21
Subject/Key Words:
National Science Foundation (NSF), Analysis of Covariance (ANCOVA), Mathematical Formulas, Multivariate Analysis, Statistical Analysis

Abstract

The relative efficiency of maximum likelihood estimates is studied when taking advantage of underlying linear patterns in the covariances or correlations when estimating covariance matrices. We compare the variances of estimates of the covariance matrix obtained under two nested patterns with the assumption that the more restricted pattern is the true state. Formulas for the asymptotic variances are given which are exact for linear covariance patterns when explicit maximum likelihood estimates exist. Several specific examples are given using complete symmetry, circular symmetry and general covariance patterns as well as an example involving a covariance matrix with a linear pattern in the correlations. (21pp.)

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