Regression and the Moore-Penrose Pseudoinverse

Name: Regression and the Moore-Penrose Pseudoinverse
Brand: Academic Press
Price: 60.95 EUR
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Albert(Autor*in)

Albert(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

195 Seiten

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Front Cover
Regression and the Moore-Penrose Pseudoinverse
Copyright Page
Contents
Preface
Acknowledgments
Part I: THE GENERAL THEORY AND COMPUTATIONAL METHODS
Chapter I. Introduction
Chapter II. General Background Material
2.1 Theorem
2.2 Theorem
2.3 Theorem
2.4 Exercise
2.5 Exercises
2.6 Theorem
2.7 Theorem
2.8 The Gram-Schmidt Orthogonalization Procedure
2.9 Exercises
2.10 Theorem
2.11 Theorem
2.12 Theorem
2.13 Theorem
2.14 Theorem
Chapter III. Geometric and Analytic Properties of the Moore-Penrose Pseudoinverse
3.1 Theorem
3.2 Theorem
3.3 Lemma
3.4 Theorem
3.5 Corollary
3.6 The Special Case of Symmetric Matrices
3.7 Exercises
3.8 Theorem
3.9 Theorem
3.10 Exercise
3.11 Exercise
3.12 Theorem
3.13 Exercises
3.14 Exercises
3.15 Theorem
3.16 Exercise
3.17 Exercise
3.18 Exercise
3.19 Exercise
Chapter IV. Pseudoinverses of Partioned Matrices and Sums and Products of Matrices
4.1 Theorem
4.2 Theorem
4.3 Theorem
4.4 Application to Stepwise Regression
4.5 Exercise
4.6 Theorem
4.7 Theorem
4.8 Theorem
4.9 Theorem
4.10 The Concept of Rank
4.11 Theorem
4.12 Theorem
4.13 Exercise
4.14 Exercise
4.15 Exercise
Chapter V. Computational Methods
5.1 Gramm-Schmidt Method of Rust, Burrus, and Schneeburger
5.2 Gauss-Jordan Elimination Method of Ben-Israel and Wersan and Noble
5.3 Gradient Projection Method of Pyle
5.4 Cayley-Hamilton Method of Decell, Ben-Israel, and Chames
Part II: STATISTICAL APPLICATIONS
Chapter VI. The General Linear Hypothesis
6.1 Best Linear Unbiased Estimation
The Gauss-Markov Theorem
6.2 Distribution for Quadratic Forms in Normal Random Variables
6.3 Estimable Vector Parametric Functions and Confidence Ellipsoids in the Case of Normal Residuals
6.4 Tests of the General Linear Hypothesis
6.5 The Relationship between Confidence Ellipsoids for Gx and Tests of the General Linear Hypothesis
6.6 Orthogonal Designs
Chapter VII. Constrained Least Squares, Penalty Functions, and BLUE's
7.1 Penalty Functions
7.2 Constrained Least Squares as Limiting Cases of BLUE's
Chapter VIII. Recursive Computation of Least Squares Estimators
8.1 Unconstrained Least Squares
8.2 Recursive Computation of Residuals
8.3 Weighted Least Squares
8.4 Recursive Constrained Least Squares, I
8.5 Recursive Constrained Least Squares, II
8.6 Additional Regressors, II (Stepwise Regression)
8.7 Relationship between Analysis of Variance and Analysis of Covariance
8.8 Missing Observations
Chapter IX. Nonnegative Definite Matrices, Conditional Expectation, and Kalman Filtering
9.1 Nonnegative Definiteness
9.2 Conditional Expectations for Normal Random Variables
9.3 Kalman Filtering
9.4 The Relationship between Least Squares Estimates and Conditional Expectations
References
Index

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