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Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface pp 223–244Cite as

Orthogonalization-Triangularization Methods in Statistical Computations

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Abstract

Procedures for reducing a data matrix to triangular form using orthogonal transformations are presented, e.g., Householder, Givens, and examples these procedures are compard to procedure operating on normal equations. We show how an analysis of variance can be constructed from the triangular reduction of the data matrix. Procedures for calculating sums of squares, degrees of freedom, and expected mean squares are presented. These procedures apply even with mixed models and missing data. It is demonstrated that all statistics needed for inference on linear combinations of parameters of a linear model may be calculated from the triangular reduction of the data matrix. Also included is a test for estimability. We also demonstrate that if the computations are done properly some inference is warranted even when the X matrix is ill-conditioned.

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Author information

Authors and Affiliations

  1. Brigham Young University, USA

    Del T. Scott & G. Rex Bryce

  2. University of Kentucky, USA

    David M. Allen

Authors
  1. Del T. Scott
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  2. G. Rex Bryce
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  3. David M. Allen
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Editor information

Editors and Affiliations

  1. Department of Statistics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    William F. Eddy

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© 1981 Springer-Verlag New York Inc.

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Scott, D.T., Bryce, G.R., Allen, D.M. (1981). Orthogonalization-Triangularization Methods in Statistical Computations. In: Eddy, W.F. (eds) Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9464-8_33

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  • DOI: https://doi.org/10.1007/978-1-4613-9464-8_33

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90633-1

  • Online ISBN: 978-1-4613-9464-8

  • eBook Packages: Springer Book Archive

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