Matrix Tricks for Linear Statistical Models Our Personal Top Twenty /

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 f...

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Détails bibliographiques
Cote:Libro Electrónico
Auteurs principaux: Puntanen, Simo (Auteur), Styan, George P. H. (Auteur), Isotalo, Jarkko (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Édition:1st ed. 2011.
Sujets:
Statistics .
Statistical Theory and Methods.
Accès en ligne:Texto Completo
Table des matières:
  • Introduction
  • 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 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 M
  • Disjointness of Column Spaces
  • Full Rank Decomposition
  • Eigenvalue Decomposition
  • Singular Value Decomposition
  • The Cauchy-Schwarz Inequality
  • Notation
  • References
  • Author Index
  • Subject Index.

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