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Cover: 9783030320997 | Plane Answers to Complex Questions | The Theory of Linear Models
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Plane Answers to Complex Questions
The Theory of Linear Models
Taschenbuch von Ronald Christensen
Sprache: Englisch

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Beschreibung
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.
Über den Autor
Ronald Christensen is a Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, former Chair of the ASA Section on Bayesian Statistical Science and former Editor of The American Statistician. His book publications include Advanced Linear Modeling (Springer, new edition forthcoming), Log-Linear Models and Logistic Regression (Springer 1997), Analysis of Variance, Design, and Regression (1996, 2016), and Bayesian Ideas and Data Analysis (2010, with Johnson, Branscum and Hanson).
Zusammenfassung

Features exercises throughout, with additional exercises supplied at the end of each chapter so that readers can retain theory

Illustrates the practical application of the projective approach to linear models

Includes appendices that with prerequisite background information on linear algebra and mathematical statistics

Prepared in conjunction with a new edition of Christensen's Advanced Linear Modeling, so that advanced undergraduate and graduate students have access to a wealth of revised content in statistical theory

Provides access to accompanying computer code

Includes supplementary material: [...]

Inhaltsverzeichnis
1. Introduction.- 2. Estimation.- 3. Testing.- 4. One-Way ANOVA.- 5. Multiple Comparison Techniques.- 6. Regression Analysis.- 7. Multifactor Analysis of Variance.- 8. Experimental Design Models.- 9. Analysis of Covariance.- 10. General Gauss-Markov Models.- 11. Split Plot Models.- 12. Model Diagnostics.- 13. Collinearity and Alternative Estimates.- 14. Variable Selection.- Appendix A - 6.- References.- Index.- Author Index.
Details
Erscheinungsjahr: 2021
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Springer Texts in Statistics
Inhalt: xxii
529 S.
33 s/w Illustr.
529 p. 33 illus.
ISBN-13: 9783030320997
ISBN-10: 3030320995
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Christensen, Ronald
Auflage: 5th ed. 2020
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Springer Texts in Statistics
Maße: 235 x 155 x 30 mm
Von/Mit: Ronald Christensen
Erscheinungsdatum: 26.08.2021
Gewicht: 0,826 kg
Artikel-ID: 119661538
Über den Autor
Ronald Christensen is a Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, former Chair of the ASA Section on Bayesian Statistical Science and former Editor of The American Statistician. His book publications include Advanced Linear Modeling (Springer, new edition forthcoming), Log-Linear Models and Logistic Regression (Springer 1997), Analysis of Variance, Design, and Regression (1996, 2016), and Bayesian Ideas and Data Analysis (2010, with Johnson, Branscum and Hanson).
Zusammenfassung

Features exercises throughout, with additional exercises supplied at the end of each chapter so that readers can retain theory

Illustrates the practical application of the projective approach to linear models

Includes appendices that with prerequisite background information on linear algebra and mathematical statistics

Prepared in conjunction with a new edition of Christensen's Advanced Linear Modeling, so that advanced undergraduate and graduate students have access to a wealth of revised content in statistical theory

Provides access to accompanying computer code

Includes supplementary material: [...]

Inhaltsverzeichnis
1. Introduction.- 2. Estimation.- 3. Testing.- 4. One-Way ANOVA.- 5. Multiple Comparison Techniques.- 6. Regression Analysis.- 7. Multifactor Analysis of Variance.- 8. Experimental Design Models.- 9. Analysis of Covariance.- 10. General Gauss-Markov Models.- 11. Split Plot Models.- 12. Model Diagnostics.- 13. Collinearity and Alternative Estimates.- 14. Variable Selection.- Appendix A - 6.- References.- Index.- Author Index.
Details
Erscheinungsjahr: 2021
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Springer Texts in Statistics
Inhalt: xxii
529 S.
33 s/w Illustr.
529 p. 33 illus.
ISBN-13: 9783030320997
ISBN-10: 3030320995
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Christensen, Ronald
Auflage: 5th ed. 2020
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Springer Texts in Statistics
Maße: 235 x 155 x 30 mm
Von/Mit: Ronald Christensen
Erscheinungsdatum: 26.08.2021
Gewicht: 0,826 kg
Artikel-ID: 119661538
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