26
Views
1
CrossRef citations to date
0
Altmetric
Statistical Computing

Orthogonalization–Triangularization Methods in Statistical Computations

, &
Pages 128-135 | Received 01 Dec 1981, Published online: 12 Mar 2012

References

  • Allen , D. M. 1974 . “Estimability, Estimates, and Variances for Linear Models,” , Cornell University, Biometrics Unit . Technical Report BU-529-M
  • Allen , D. M. “Computational Methods for Estimation of Linear Combinations of Parameters,” . Proceedings of the Statistical Computing Section . pp. 1 – 6 . American Statistical Association .
  • Banachiewicz , T. 1937 . “Calcul des Déterminants par la Méthode des Eracouiens,” , 109 – 120 . Academie Polonaies des Sciences Bulletin Serie des Sciences Mathematiques Astronomiques et Physiquer .
  • Beaton , A. B. 1964 . “The Use of Special Matrix Operators in Statistical Calculus,” , Princeton , NJ : Educational Testing Service . Technical Report RB-64–51
  • Belsley , D. A. , Kuh , E. and Welsh , R. E. 1980 . Regression Diagnostics , New York : John Wiley .
  • Benoit . 1924 . “Note sur une Méthode de Résolution des Équations Normales,” . Bulletin Geodesique , 2 : 5 – 77 .
  • Bowen , W. M. 1976 . “A Comparison of Six Methods for Estimating Variance Components From Random Models in Non-Orthogonal Two-Way Designs,” , Brigham Young University, Dept. of Statistics . unpublished master's thesis
  • Boyer , C. B. 1968 . A History of Mathematics , New York : John Wiley .
  • Bryce , G. R. , Carter , M. W. and Scott , D. T. “Reparameterization of the Cell Means Model and the Calculation of Expected Mean Squares,” . Proceedings of the Statistical Computing Section . pp. 45 – 54 . American Statistical Association .
  • Bryce , G. R. , Carter , M. W. and Scott , D. T. 1980 . “Recovery of Estimability in Fixed Models With Missing Cells,” , Brigham Young University, Dept. of Statistics . Technical Report SD-0220R
  • Bryce , G. R. , Scott , D. T. and Carter , M. W. 1980 . “Estimation and Hypotheses Testing in Linear Models–A Reparameterization Approach to the Cell Means Models,” . Communications in Statistics–Theory and Methods , 9 : 131 – 150 . Ser. A
  • Chakravarti , I. M. , Laha , R. G. and Roy , J. 1967 . Handbook of Methods of Applied Statistics , Vol. 1 , New York : John Wiley .
  • Chambers , J. M. 1977 . Computational Methods for Data Analysis , New York : John Wiley .
  • Cummings , W. G. and Gaylor , D. W. 1974 . “Variance Component Testing in Unbalanced Nested Designs,” . Journal of the American Statistical Association , 69 : 765 – 771 .
  • Doolittle , M. H. 1878 . “Method Employed in the Solution of Normal Equations and the Adjustment of a Triangulation,” . In U.S. Coast and Geodetic Survey Report , 115 – 120 . Washington , DC : Government Printing Office .
  • Dwyer , P. S. 1941 . “The Doolittle Technique,” . Annals of Mathematical Statistics , 12 : 449 – 458 .
  • Dwyer , P. S. 1944 . “A Matrix Presentation of Least Squares and Correlation Theory With Matrix Justification of Improved Methods of Solution,” . Annals of Mathematical Statistics , 15 : 82 – 89 .
  • Dwyer , P. S. 1945 . “The Square Root Method and Its Use in Correlation and Regression,” . Journal of the American Statistical Association , 40 : 493 – 503 .
  • Dwyer , P. S. 1951 . Linear Computations , New York : John Wiley .
  • Francis , I. 1973 . “A Comparison of Several Analysis of Variance Programs,” . Journal of the American Statistical Association , 68 : 860 – 871 .
  • Gauss , C. F. 1873 . “Supplementom Theoriae Combinationis Observationum Erroribus Minimis Obnoxiae,” . In Werke (Vol. 15) , Göettingen : Vandenhoeck and Ruprecht .
  • Gaylor , D. W. , Lucas , H. L. and Anderson , R. L. 1970 . “Calculation 223of Expected Mean Squares by the Abbreviated Doolittle and Square Root Methods,” . Biometrics , 26 : 641 – 655 .
  • Gentleman , W. M. 1973 . “Least Squares Computations by Givens Transformations Without Square Roots,” . Journal of Instructional Mathematics and Applications , 2 : 329 – 336 .
  • Givens , W. 1954 . “Numerical Computation of the Characteristic Values of a Real Symmetric Matrix,” , Oak Ridge , TN : Oak Ridge National Laboratories . Technical Report ORNL-1574
  • Goodnight , J. H. 1979 . “A Tutorial on the Sweep Operator,” . The American Statistician , 33 : 149 – 158 .
  • Graybill , F. A. 1969 . Introduction to Matrices With Applications in Statistics , Belmont , CA : Wadsworth .
  • Graybill , F. A. 1976 . Theory and Application of the Linear Model , North Scituate , MA : Duxbury Press .
  • Hartley , H. O. 1967 . “Expectations, Variances and Covariances of ANOVA Mean Squares by ‘Synthesis',” . Biometrics , 23 : 105 – 114 .
  • Hocking , R. R. and Speed , F. M. 1975 . “A Full Rank Analysis of Some Linear Model Problems,” . Journal of the American Statistical Association , 70 : 706 – 712 .
  • Hocking , R. R. , Hackney , O. P. and Speed , F. M. 1978 . “The Analysis of Linear Models With Unbalanced Data,” . In Contributions to Survey Sampling and Applied Statistics , 133 – 152 . New York : Academic Press .
  • Householder , A. S. 1958 . “Unitary Triangularization of a Non-Symmetric Matrix,” . Journal of the Association for Computing Machinery , 5 : 339 – 342 .
  • Kennedy , W. J. and Gentle , J. E. 1980 . Statistical Computing , New York : Marcel Dekker .
  • Kutner , M. H. 1974 . “Hypotheses Testing in Linear Models,” . The American Statistician , 28 : 98 – 100 .
  • Lawson , C. L. and Hanson , R. J. 1974 . Solving Least Squares Problems , Englewood Cliffs , NJ : Prentice-Hall .
  • Lucas , H. L. 1950 . “A Method of Estimating Components of Variance in Disproportionate Numbers,” . Annals of Mathematical Statistics , 21 : 304
  • Rohde , C. A. and Harvey , J. R. 1965 . “Unified Least Squares Analyses,” . Journal of the American Statistical Association , 60 : 523 – 527 .
  • Schur , J. 1917 . “Uber Potenzreihen due cm Innern des Einheitskreises Beschrankt Sind,” . Crelle's Journal Fuer Reine und Angewandte Mathematik , 147 : 205 – 232 .
  • Scott , D. T. , Bryce , G. R. and Allen , D. M. “Orthogonalization–Triangularization Methods in Statistical Computations,” . Proceedings of the 13th Symposium on the Interface . pp. 223 – 244 . New York : Springer-Verlag .
  • Searle , S. R. 1971 . Linear Models , New York : John Wiley .
  • Searle , S. R. , Milliken , G. A. and Speed , F. M. 1979 . “Expected Marginal Means in the Linear Model,” , Cornell University, Biometrics Unit . Technical Report BU-672-M
  • Seber , G. A. F. 1977 . Linear Regression Analysis , New York : John Wiley .
  • Speed , F. M. “Choice of Sums of Squares for Estimation of Components of Variance,” . Proceedings of the Statistical Computing Section . pp. 55 – 58 . American Statistical Association .
  • Speed , F. M. and Hocking , R. R. 1974 . “Computations of Expectations, Variances and Covariances of ANOVA Mean Squares,” . Biometrics , 30 : 156 – 169 .
  • Speed , F. M. , Hocking , R. R. and Hackney , O. P. 1978 . “Methods of Analysis of Linear Models With Unbalanced Data,” . Journal of the American Statistical Association , 73 : 105 – 112 .
  • Stewart , G. W. 1973 . Introduction to Matrix Computations , New York : Academic Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.