Open Access
Issue
Genet. Sel. Evol.
Volume 40, Number 1, January-February 2008
Page(s) 3 - 24
DOI https://doi.org/10.1051/gse:2007032
Published online 21 December 2007
References of  Genet. Sel. Evol. 40 (2008) 3-24
  1. Boyd S., Vandenberghe L., Convex Optimization, Cambridge University Press (2004).
  2. Cullis B.R., Smith A.B., Thompson R., Perspectives of ANOVA, REML and a general linear mixed model, in: Methods and Models in Statistics in Honour of Professor John Nelder, FRS, Imperial College Press, London, 2004, pp. 53-94.
  3. Dempster A.P., Laird N.M., Rubin D.B., Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Stat. Soc. B 39 (1977) 1-39.
  4. Dennis J.E., Schnabel R.B., Numerical methods for Unconstrained Optimization and Nonlinear Equations, SIAM Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 1996.
  5. Forsgren A., Gill P.E., Murray W., Computing modified Newton directions using a partial Cholesky factorization, SIAM J. Sci. Statist. Comp. 16 (1995) 139-150 [CrossRef].
  6. Foulley J.L., van Dyk D.A, The PX-EM algorithm for fast stable fitting of Henderson's mixed model, Genet. Sel. Evol. 32 (2000) 143-163 [CrossRef] [PubMed] [EDP Sciences].
  7. Groeneveld E., A reparameterisation to improve numerical optimisation in multivariate REML (co)variance component estimation, Genet. Sel. Evol. 26 (1994) 537-545 [CrossRef] [EDP Sciences].
  8. Harville D.A., Maximum likelihood approaches to variance component estimation and related problems, J. Amer. Stat. Ass. 72 (1977) 320-338 [CrossRef].
  9. Harville D.A., Matrix Algebra from a Statistician's Perspective, Springer Verlag, 1997.
  10. Henderson C.R., A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values, Biometrics 32 (1976) 69-83 [CrossRef].
  11. Henderson C.R., Estimation of variances and covariances under multiple trait models, J. Dairy Sci. 67 (1984) 1581-1589.
  12. Jamshidian M., Jennrich R.I, Conjugate gradient acceleration of the EM algorithm, J. Amer. Stat. Ass. 88 (1993) 221-228 [CrossRef].
  13. Jamshidian M., Jennrich R.I., Acceleration of the EM algorithm using Quasi-Newton methods, J. Roy. Stat. Soc. B 59 (1997) 569-587 [CrossRef].
  14. Jennrich R.I., Sampson P.F., Newton-Raphson and related algorithms for maximum likelihood variance component estimation, Technometrics 18 (1976) 11-17 [CrossRef] [MathSciNet].
  15. Jennrich R.I., Schluchter M.D., Unbalanced repeated-measures models with structured covariance matrices, Biometrics 42 (1986) 805-820 [CrossRef] [PubMed] [MathSciNet].
  16. Kirkpatrick M., Meyer K., Simplified analysis of complex phenotypes: Direct estimation of genetic principal components, Genetics 168 (2004) 2295-2306 [CrossRef] [PubMed].
  17. Laird N., Lange N., Stram D., Maximum likelihood computations with repeated measures: applications of the EM algorithm, J. Amer. Stat. Ass. 82 (1987) 97-105 [CrossRef].
  18. Lange K., A gradient algorithm locally equivalent to the EM algorithm, J. Roy. Stat. Soc. B 57 (1995) 425-438.
  19. Lindstrom M.J., Bates D.M., Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data, J. Amer. Stat. Ass. 83 (1988) 1014-1022 [CrossRef].
  20. Liu C., Rubin D.B., Wu Y.N., Parameter expansions to accelerate EM: The PX-EM algorithm, Biometrika 85 (1998) 755-770 [CrossRef] [MathSciNet].
  21. McLachlan G.J., Krishnan T., The EM algorithm and extensions, Wiley Series in Probability and Statistics, Wiley, New York, 1997.
  22. Meilijson I., A fast improvement of the EM algorithm on its own terms, J. Roy. Stat. Soc. B 51 (1989) 127-138.
  23. Meng X.L., van Dyk D., The EM algorithm - an old folk-song sung to a new fast tune, J. Roy. Stat. Soc. B 59 (1997) 511-567 [CrossRef].
  24. Meng X.L., van Dyk D., Fast EM-type implementations for mixed-effects models, J. Roy. Stat. Soc. B 60 (1998) 559-578 [CrossRef].
  25. Meyer K., Random regressions to model phenotypic variation in monthly weights of Australian beef cows, Livest. Prod. Sci. 65 (2000) 19-38 [CrossRef].
  26. Meyer K., Advances in methodology for random regression analyses, Austr. J. Exp. Agric. 45 (2005a) 847-858 [CrossRef].
  27. Meyer K., Genetic principal components for live ultra-sound scan traits of Angus cattle, Anim. Sci. 81 (2005b) 337-345 [CrossRef].
  28. Meyer K., PX $\times$ AI: algorithmics for better convergence in restricted maximum likelihood estimation, CD-ROM Eighth World Congr. Genet. Appl. Livest. Prod., August 13-18 2006, Belo Horizonte, Brasil, Communication No. 24-15.
  29. Meyer K., Kirkpatrick M., Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices, Genet. Sel. Evol. 37 (2005) 1-30 [CrossRef] [PubMed] [EDP Sciences].
  30. Meyer K., Kirkpatrick M., A note on bias in reduced rank estimates of covariance matrices, Proc. Ass. Advan. Anim. Breed. Genet. 17 (2007) 154-157.
  31. Meyer K., Smith S.P., Restricted maximum likelihood estimation for animal models using derivatives of the likelihood, Genet. Sel. Evol. 28 (1996) 23-49 [CrossRef] [EDP Sciences].
  32. Meyer K., Carrick M.J., Donnelly B.J.P., Genetic parameters for growth traits of Australian beef cattle from a multi-breed selection experiment, J. Anim. Sci. 71 (1993) 2614-2622 [PubMed].
  33. Neumaier A., Groeneveld E., Restricted maximum likelihood estimation of covariance components in sparse linear models, Genet. Sel. Evol. 30 (1998) 3-26 [CrossRef] [EDP Sciences].
  34. Ng S.K., Krishnan T., McLachlan G.J., The EM algorithm, in: Gentle J.E., Härdle W., Mori Y., (Eds.), Handbook of Computational Statistics, vol. I, Springer Verlag, New York, 2004, pp. 137-168.
  35. Nocedahl J., Wright S.J., Numerical Optimization, Springer Series in Operations Research, Springer Verlag, New York, Berlin Heidelberg, 1999.
  36. Pinheiro J.C., Bates D.M., Unconstrained parameterizations for variance-covariance matrices, Stat. Comp. 6 (1996) 289-296 [CrossRef].
  37. Schnabel R.B., Estrow E., A new modified Cholesky factorization, SIAM J. Sci. Statist. Comp. 11 (1990) 1136-1158 [CrossRef].
  38. Thompson R., Meyer K., Estimation of variance components: What is missing in the EM algorithm? J. Stat. Comp. Simul. 24 (1986) 215-230 [CrossRef].
  39. Thompson R., Cullis B.R., Smith A.B., Gilmour A.R., A sparse implementation of the Average Information algorithm for factor analytic and reduced rank variance models, Austr. New Zeal. J. Stat. 45 (2003) 445-459 [CrossRef].
  40. Thompson R., Brotherstone S., White I.M.S., Estimation of quantitative genetic parameters, Phil. Trans. R. Soc. B 360 (2005) 1469-1477 [CrossRef].
  41. van Dyk D.A., Fitting mixed-effects models using efficient EM-type algorithms, J. Comp. Graph. Stat. 9 (2000) 78-98 [CrossRef].