Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

INFLUENCE ANALYSIS OF CHOLESKY DECOMPOSITION

  • Received : 2009.10.20
  • Accepted : 2010.01.08
  • Published : 2010.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

Keywords

References

  1. V. Barnett and T. Lewis, Outliers in Statistical Data, 3rd Ed., John Wiley & Sons, 1994
  2. S. Chatterjee and A. S. Hadi, Sensitivity Analysis in Linear Regression, Wiley, New York, 1988
  3. V. De Gruttola, J. H. Ware and T. A. Louis, Influence analysis of generalized least squares estimators, Journal of the American Statistical Association, 82 (1987), 911-917 https://doi.org/10.2307/2288804
  4. R. L. Dykstra, Establishing the positive definiteness of the sample covariance matrix, Annals of Mathematical Statistics, 41 (1970), 2153-2154 https://doi.org/10.1214/aoms/1177696719
  5. D. M. Hawkins and W. J. R. Eplett, The Cholesky factorization of the inverse correlation or covariance matrix in multiple regression, Technometrics, 24 (1982), 191-197 https://doi.org/10.2307/1268678
  6. A. J. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, Englewood Cliffs: Prentice-Hall, 1992
  7. M. G. Kim, Influence curve for the Cholesky root of a covariance matrix, Communications in Statistics: Theory and Methods, 23 (1994), 1399-1412 https://doi.org/10.1080/03610929408831330
  8. M. G. Kim, Multivariate outliers and decompositions of Mahalanobis distance, Communications in Statistics: Theory and Methods, 29 (2000), 1511-1526 https://doi.org/10.1080/03610920008832559
  9. M. J. Lindstrom and D. M. Bates, Newton-Raphson and EM algorithm for linear mixed effects models for repeated measures data, Journal of the American Statistical Association, 83 (1988), 1014-1022 https://doi.org/10.2307/2290128
  10. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons, 1988
  11. M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation, Biometrika, 86 (1999), 677-690 https://doi.org/10.1093/biomet/86.3.677
  12. M. Pourahmadi, Cholesky decompositions and estimation of a covariance matrix: orthogonality of variance-correlation parameters, Biometrika, 94 (2007), 1006-1013 https://doi.org/10.1093/biomet/asm073
  13. G. W. Stewart, Introduction to Matrix Computations, Academic Press, 1973