UID:
almahu_9949697888802882
Format:
1 online resource (195 p.)
ISBN:
1-282-29012-6
,
9786612290121
,
0-08-095603-3
Series Statement:
Mathematics in science and engineering ; v. 94
Content:
Regression and the Moore-Penrose pseudoinverse
Note:
Description based upon print version of record.
,
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
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3.5 Corollary3.6 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
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Chapter V. Computational Methods5.1 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
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6.4 Tests of the General Linear Hypothesis6.5 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
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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
,
English
Additional Edition:
ISBN 0-12-048450-1
Language:
English
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