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The Coordinate-Free Approach to Linear Models

The Coordinate-Free Approach to Linear Models

$75.99 (C)

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: October 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521868426

$ 75.99 (C)

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About the Authors
  • This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with nonrandom predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered include inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and nonoptimal properties of Gauss-Markov, Bayes, and shrinkage estimators under the assumption of normality, the optimal properties of F-tests, and the analysis of covariance and missing observations.

    • Geometric approach to linear statistical models
    • Optimality theory
    • Many exercises and problems; detailed index
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    Reviews & endorsements

    "The index of the book is excellent... The book will be useful for students (and researchers) of statistics to learn another, and possibly more insightful, approach to linear modeling."
    M. Huskova, Mathematical Reviews

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    Product details

    • Date Published: October 2006
    • format: Hardback
    • isbn: 9780521868426
    • length: 214 pages
    • dimensions: 254 x 178 x 13 mm
    • weight: 0.59kg
    • contains: 7 tables
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Topics in linear algebra
    3. Random vectors
    4. Gauss-Markov estimation
    5. Normal theory: estimation
    6. Normal theory: testing
    7. Analysis of covariance
    8. Missing observations.

  • Author

    Michael J. Wichura, University of Chicago
    Professor Wichura has 37 years of teaching experience in the Department of Statistics at the University of Chicago. He has served as an Associate Editor for the Annals of Probability and was the Database Editor for the Current Index to Statistics from 1995 to 2000. He is the author of the PiCTeX macros (for drawing pictures in TeX) and the PiCTeX manual, and also of the TABLE macros and the TABLE manual.

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