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...
| Main Authors: | , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2011, 2011
|
| Edition: | 1st ed. 2011 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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