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© 2011

Matrix Tricks for Linear Statistical Models

Our Personal Top Twenty

Book

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 1-56
  3. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 57-70
  4. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 71-90
  5. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 91-104
  6. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 105-120
  7. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 121-144
  8. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 145-150
  9. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 151-154
  10. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 155-190
  11. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 191-214
  12. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 215-266
  13. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 267-282
  14. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 283-290
  15. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 291-304
  16. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 305-316
  17. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 317-342
  18. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 343-348
  19. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 349-356
  20. Simo Puntanen, George P. H. Styan, Jarkko Isotalo
    Pages 357-390

About this book

Introduction

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result.
In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.

Keywords

Löwner ordering Schur complement best linear unbiased estimation generalized inverse orthogonal projector singular value decomposition

Authors and affiliations

  1. 1.Dept. Mathematics, Statistics &, PhilosophyUniversity of TampereTampereFinland
  2. 2.Dept. Mathematics & StatisticsMcGill UniversityMontrealCanada
  3. 3.Dept. Mathematics, Statistics &, PhilosophyUniversity of TampereTampereFinland

About the authors

Simo Puntanen earned his PhD in statistics from the University of Tampere (Tampere, Finland) in 1987, where he is now a Docent and Lecturer of Statistics. He has published over 110 research papers in matrix methods for statistics with particular emphasis on linear statistical models. He is currently the book review editor of the International Statistical Review.

George P. H. Styan earned his PhD in mathematical statistics from Columbia University in 1969 and received an Honorary PhD from the University of Tampere in 2000. He is now Professor Emeritus of Mathematics and Statistics at McGill University in  Montreal, Canada. He has published over 140 research papers, mostly in matrix methods for statistics, and since 2005, his main interests have focused on magic squares, and mathematical and statistical philately.

Jarkko Isotalo earned his PhD in statistics from the University of Tampere (Tampere, Finland) in 2007, where he is now a Lecturer of Statistics. His main research interests have been linear statistical models, matrix methods for statistics, and computational statistics. He is currently also doing applied research on statistical genetics.

Puntanen, Styan, and Isotalo, knowing just what is expected of authors, would like to agree with P. G. Wodehouse and apologize for childhoods that were as normal as rice-pudding and lives that consisted of little more than sitting in front of the laptop and cursing a bit.


Bibliographic information

  • Book Title Matrix Tricks for Linear Statistical Models
  • Book Subtitle Our Personal Top Twenty
  • Authors Simo Puntanen
    George P. H. Styan
    Jarkko Isotalo
  • DOI https://doi.org/10.1007/978-3-642-10473-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-642-10472-5
  • Softcover ISBN 978-3-642-44759-4
  • eBook ISBN 978-3-642-10473-2
  • Edition Number 1
  • Number of Pages XVII, 486
  • Number of Illustrations 35 b/w illustrations, 35 illustrations in colour
  • Topics Statistical Theory and Methods
  • Buy this book on publisher's site
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Reviews

From the reviews:

“It is for everyone who works on the properties of (multivariate) linear statistical models, especially for graduate students in statistics. Also, the book is … for experts who have had an introduction to multivariate models and have a big preference for matrix results. … book is full of recent results and advances of linear algebra related linear statistical models over the last decades. … book has the potential to become a major reference book for further developments of estimators of linear models in the future.” (Wolfgang Polasek, International Statistical Review, Vol. 81 (1), 2013)

“This new book is closely connected with matrices and linear models … . the authors extract from the matrix algebra and theory of linear models twenty key results or ideas which they call ‘tricks’. … This exceptional book can be recommended to all interested students who wish to improve their skills in linear models and matrix manipulations. It can be recommended also to professors teaching statistics who may utilize this book as a rich source of various exercises, references and interesting historical notes.” (Radosław Kala, IMAGE, Issue 48, Spring, 2012)