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Common Principal Components for Dependent Random Vectors

✍ Scribed by Beat E Neuenschwander; Bernard D Flury

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 186 KB
Volume: 75
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.2000.1908

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✦ Synopsis

Let the kp-variate random vector X be partitioned into k subvectors X i of dimension p each, and let the covariance matrix 9 of X be partitioned analogously into submatrices 9 ij . The common principal component (CPC) model for dependent random vectors assumes the existence of an orthogonal p by p matrix ; such that ; t 9 ij ; is diagonal for all (i, j ). After a formal definition of the model, normal theory maximum likelihood estimators are obtained. The asymptotic theory for the estimated orthogonal matrix is derived by a new technique of choosing proper subsets of functionally independent parameters.

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We consider sequences of length m of n-tuples each with k nonzero entries chosen randomly from an Abelian group or finite field. For what values of m does there exist a subsequence which is zero-sum or linearly dependent, respectively? We report some results relating to these problems.