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Activity Number: 219
Type: Topic Contributed
Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract #311239
Title: Kronecker-Product Variance-Covariance Structures: Some Important Elements of Estimation and Testing
Author(s): Pierre Dutilleul*+
Companies: McGill University
Keywords:
Abstract:

Some of the results to be presented are from recent joint work with Ameur M. Manceur; the others are from my own work. The Kronecker-product variance-covariance structures considered for analysis are general in that the factor matrices are positive definitive without any other particular constraint, i.e. each factor matrix is of unstructured type. The key points that I shall address include the following. On the estimation side: In the absence of analytical solutions for the system of likelihood equations, the MLE (alias 'flip-flop') algorithm is solved for the matrix and tensor (alias 'multilinear') normal distributions; in some identified cases, the solutions of the algorithm are not the only matrix estimates that maximize the likelihood function. On the testing side: The likelihood-ratio test (LRT) for variance-covariance matrices has long been known to be biased, because of too large a number of degrees of freedom for the approximating asymptotic chi-square distribution; in modified LRTs for simple and double separability, a penalty factor which applies to the test statistic and whose value changes with the mean model provides unbiasedness to the testing procedure.


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