On Computing a Cholesky Decomposition

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

초록

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.

키워드

참고문헌

  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.