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On the existence of positive-definite maximum-likelihood estimates of structured covariance matrices

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2 Author(s)
Fuhrmann, D.R. ; Electron. Syst. & Signals Res. Lab., Washington Univ., St. Louis, MO, USA ; Miller, M.I.

It is shown that a sufficient condition for the likelihood function of a zero-mean Gaussian random vector with covariance R from some class of covariances R to be unbounded above over the set of positive-definite matrices in R is that some singular Ro exists in R whose range space contains the data. The results obtained imply that, for the spectrum estimation problem in which R is the class of Toeplitz covariances and only one long observation vector is available, by constraining the maximum-likelihood estimation problem to the class of Toeplitz matrices with nonnegative definite circulant extensions, a positive-definite solution is guaranteed to exist

Published in:

Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 4 )

Date of Publication:

Jul 1988

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