Regression and the Moore-Penrose pseudoinverse / Arthur Albert.

Format:

Book

Author/Creator:

Albert, Arthur E.

Series:

Mathematics in science and engineering ; v. 94.

Mathematics in science and engineering ; v. 94

Language:

English

Subjects (All):

Matrix inversion.

Regression analysis.

Physical Description:

1 online resource (195 p.)

Other Title:

Moore-Penrose pseudoinverse.

Place of Publication:

New York : Academic Press, 1972.

Language Note:

English

Summary:

Regression and the Moore-Penrose pseudoinverse

Contents:

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 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

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

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

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-29012-6

9786612290121

0-08-095603-3

OCLC:

466442527