Matrix tricks for linear statistical models : our personal top twenty / Simo Puntanen, George P.H. Styan, Jarkko Isotalo.

By: Puntanen, Simo
Contributor(s): Styan, George Peter Hansbenno | Isotalo, Jarkko
Material type: TextTextLanguage: English Publisher: Berlin ; New York : Springer, c2011Description: xvii, 486 p. : ill. ; 24 cmISBN: 9783642104725 (hbk.); 364210472X (hbk.)Subject(s): Linear models (Statistics) | Matrix analytic methodsDDC classification: 519.535 LOC classification: QA276 | .P83 2011Online resources: WorldCat details | E-book Fulltext
Contents:
Easy column space tricks -- Easy projector tricks -- Easy correlation tricks -- Generalized inverses in a nutshell -- Rank of the partitioned matrix and the matrix product -- Rank cancellation rule -- Sum of orthogonal projectors -- A decomposition of the orthogonal projector -- Minimizing cov(y -- FX) -- BLUE -- General solution to AYB=C -- Invariance with respect to the choice of generalized inverse -- Block-diagonalization and the Schur complement -- Nonnegative definiteness of a partitioned matrix -- The matrix Ṁ -- Disjointness of column spaces -- Full rank decomposition -- Eigenvalue decomposition -- Singular value decomposition -- The Cauchy-Schwarz inequality -- Notation -- List of figures and philatelic items.
Summary: Summary: 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 Read more...
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Includes bibliographical references (p. 439-468) and indexes.

Easy column space tricks --
Easy projector tricks --
Easy correlation tricks --
Generalized inverses in a nutshell --
Rank of the partitioned matrix and the matrix product --
Rank cancellation rule --
Sum of orthogonal projectors --
A decomposition of the orthogonal projector --
Minimizing cov(y --
FX) --
BLUE --
General solution to AYB=C --
Invariance with respect to the choice of generalized inverse --
Block-diagonalization and the Schur complement --
Nonnegative definiteness of a partitioned matrix --
The matrix Ṁ --
Disjointness of column spaces --
Full rank decomposition --
Eigenvalue decomposition --
Singular value decomposition --
The Cauchy-Schwarz inequality --
Notation --
List of figures and philatelic items.

Summary:
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 Read more...

Applied Statistics

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