| Description |
1 online resource (312 pages) |
| Series |
Statistics: a Series of Textbooks and Monographs ; v. 91 |
|
Statistics, textbooks and monographs.
|
| Contents |
Cover; Half Title; Title Page; Copyright Page; PREFACE; Table of Contents; 1: THE GAUSS AND GAUSS-JORDAN METHODS: ASPECTS OF COMPUTER PROGRAMMING; 1.1 Introduction; 1.2 Gauss's Method; 1.3 Gauss's Method with Row Interchanges; 1.4 The Gauss-Jordan Method; 1.5 Arithmetical Cost; 1.6 Efficient Programming; 1.7 Computer Representation of Numbers; 1.8 A Measure of Computational Accuracy; 1.9 Gauss's Method with Integer Coefficients; Exercises; References; 2: MATRIX ANALYSIS OF GAUSS'S METHOD: THE CHOLESKY AND DOOLITTLE DECOMPOSITIONS; 2.1 Matrix Representation; 2.2 Matrix Multiplication |
|
2.3 Matrix Inversion2.4 Elementary Matrices; 2.5 Matrix Analysis of Gauss's Method; 2.6 The Determinant; 2.7 Doolittle's L0U* Decomposition; 2.8 The U'0DU0 Decomposition; 2.9 Cholesky's U'U Decomposition; 2.10 Horst's Method; Exercises; References; 3: THE LINEAR ALGEBRAIC MODEL: THE METHOD OF AVERAGES AND THE METHOD OF LEAST SQUARES; 3.1 The Linear Algebraic Model; 3.2 The Method of Averages; 3.3 The Method of Least Squares; 3.4 Accuracy; 3.5 Empirical Condition Number; 3.6 Longley's Test Problem; Exercises; References; 4: THE CAUCHY-BIENAYMÉ, LAPLACE, AND SCHMIDT PROCEDURES |
|
4.1 The Cauchy-Bienaymé Procedure I4.2 The Cauchy-Bienaymé Procedure II; 4.3 The Laplace Orthogonalization Procedure; 4.4 The Schmidt Orthogonalization Procedure; 4.5 Comparison of the Schmidt and Laplace Procedures; 4.6 Laplace's Procedure with Column Interchanges; 4.7 Uniqueness of the U'0DU0 Decomposition; 4.8 Partial Orthogonalization and Scaling; Exercises; References; 5: HOUSEHOLDER'S PROCEDURE; 5.1 Householder's Procedure; 5.2 Householder's Transformation Matrix; 5.3 Comparison of the Householder and Laplace Procedures; 5.4 Further Remarks on Householder's Procedure |
|
5.5 Maindonald's Variant of Householder's Procedure5.6 Householder's Procedure with Column Interchanges; Exercises; References; 6: GIVENS'S PROCEDURE; 6.1 Givens Transformation Matrix; 6.2 Givens's Procedure; 6.3 A Revised Version of Givens's Procedure; 6.4 Partial Orthogonalization; 6.5 Square Root Free Variants of Givens's Procedure; 6.6 Gentleman's Procedure; 6.7 The Weighted Least Squares Estimator; 6.8 Deleting Observations; 6.9 Imposing Constraints; 6.10 Stirling's Procedure; 6.11 Generalized Givens Transformations with Integer Coefficients; Exercises; References |
|
7: UPDATING THE QU DECOMPOSITION7.1 Adding Rows; 7.2 Deleting Rows; 7.3 Adding Columns; 7.4 Deleting Columns; 7.5 Permuting Columns; 7.6 All Possible Regressions; 7.7 Adding Dummy Rows and Dummy Columns; Exercises; References; 8: PSEUDO-RANDOM NUMBERS; 8.1 Data Precision; 8.2 Multiplicative Congruential Pseudo-Random Number Generators; 8.3 Uniformly Distributed Pseudo-Random Numbers; 8.4 Mean and Variance; 8.5 Normally Distributed Pseudo-Random Numbers; Exercises; Project: A Simulation Study; References; 9: THE STANDARD LINEAR MODEL; 9.1 The Linear Statistical Model |
| Summary |
Presenting numerous algorithms in a simple algebraic form so that the reader can easilytranslate them into any computer language, this volume gives details of several methodsfor obtaining accurate least squares estimates. It explains how these estimates may beupdated as new information becomes available and how to test linear hypotheses. Linear Least Squares Computations features many structured exercises that guidethe reader through the available algorithms, plus a glossary of commonly used terms anda bibliography of supplementary reading . collects "ancient" and modem results onlinear least squares computations in a convenient single source . . develops the necessarymatrix algebra in the context of multivariate statistics . only makes peripheral use ofconcepts such as eigenvalues and partial differentiation . interprets canonical formsemployed in computation . discusses many variants of the Gauss, Laplace-Schmidt, Givens, and Householder algorithms . and uses an empirical approach for the appraisalof algorithms. Linear Least Squares Computations serves as an outstanding reference forindustrial and applied mathematicians, statisticians, and econometricians, as well as atext for advanced undergraduate and graduate statistics, mathematics, and econometricscourses in computer programming, linear regression analysis, and applied statistics |
| Notes |
9.2 The Expectation and Variance of a Random Variable |
|
Print version record |
| Subject |
Computational Numerical Analysis
|
| Form |
Electronic book
|
| ISBN |
9781351435260 |
|
1351435264 |
|
