Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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On Computing a Cholesky Decomposition

  • Park, Jong-Tae (Department of Computer Science & Statistics, Pyongtaek University, Pyongtaek, 450-701)
  • Published : 1996.08.01
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Abstract

Maximum likelihood estimation of Cholesky decomposition is considered under normality assumption. It is shown that maximum liklihood estimation gives a Cholesky decomposition of the sample covariance matrix. The joint distribution of the maximum likelihood estimators is derived. The ussual algorithm for a Cholesky decomposition is shown to be equivalent to a maximumlikelihood estimation of a Cholesky root when the underlying distribution is a multivariate normal one.

Keywords

References

  1. An introduction to multivariate statistical analysis(2nd Ed.) Anderson, T.W.
  2. Annals of Statistics v.15 Best equivariant estimators of a Cholesky decomposition Eaton, M.L.;Olkin, I.
  3. Matrix computations Golub, G.H.;Van, Loan, C.
  4. Linear Algebra and Its Applications v.67 Estimating a Cholesky decomposition Olkin, I.
  5. Annals of Mathematical Statistics v.37 Invariance of maximum lkielihood estimation Zehna, P.W.