Linear Models and the Relevant Distributions and Matrix Algebra

David A. Harville

March 13, 2018 by Chapman and Hall/CRC
Textbook - 524 Pages
ISBN 9781138578333 - CAT# K43718
Series: Chapman & Hall/CRC Texts in Statistical Science


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Self-contained coverage of the relevant distributions and matrix algebra

Detailed and accessible derivations or proofs of essentially all results

In-depth coverage of all included topics

Expanded coverage of predictive inference and of multiple comparisons and simultaneous confidence intervals

Extensive coverage of the optimality properties of the F test


Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context of a relatively complex setting of great practical importance.


  • Provides coverage of matrix algebra that is extensive and relatively self-contained and does so in a meaningful context
  • Provides thorough coverage of the relevant statistical distributions, including spherically and elliptically symmetric distributions
  • Includes extensive coverage of multiple-comparison procedures (and of simultaneous confidence intervals), including procedures for controlling the k-FWER and the FDR
  • Provides thorough coverage (complete with detailed and highly accessible proofs) of results on the properties of various linear-model procedures, including those of least squares estimators and those of the F test.
  • Features the use of real data sets for illustrative purposes
  • Includes many exercises

David Harville served for 10 years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories at Wright-Patterson AFB, Ohio, 20 years as a full professor in Iowa State University’s Department of Statistics where he now has emeritus status, and seven years as a research staff member of the Mathematical Sciences Department of IBM’s T.J. Watson Research Center. He has considerable relevant experience, having taught M.S. and Ph.D. level courses in linear models, been the thesis advisor of 10 Ph.D. graduates, and authored or co-authored two books and more than 80 research articles. His work has been recognized through his election as a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics and as a member of the International Statistical Institute.