Theory Of Linear Models
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Linear Model Theory
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Author : Dale L. Zimmerman
language : en
Publisher: Springer Nature
Release Date : 2020-11-02
Linear Model Theory written by Dale L. Zimmerman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Mathematics categories.
This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.
Linear Models In Statistics
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Author : Alvin C. Rencher
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-07
Linear Models In Statistics written by Alvin C. Rencher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-07 with Mathematics categories.
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
Theory Of Linear Models
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Author : Bent Jorgensen
language : en
Publisher: CRC Press
Release Date : 1993-10-01
Theory Of Linear Models written by Bent Jorgensen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-01 with Mathematics categories.
This book provides a self-contained exposition of the theory of linear models, including practical aspects of residuals and data analysis.
Plane Answers To Complex Questions
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Author : Ronald Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 1996
Plane Answers To Complex Questions written by Ronald Christensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This textbook provides a wide-ranging introduction to the use of linear models in analyzing data. The author's emphasis is on providing a unified treatment of the analysis of variance models and regression models by presenting a vector space and projections approach to the subject. Every chapter comes with numerous exercises and examples, which will make it ideal for a graduate-level course on this subject.
Linear Models
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Author : Brenton R. Clarke
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-19
Linear Models written by Brenton R. Clarke and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-19 with Mathematics categories.
An insightful approach to the analysis of variance in the study of linear models Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixed-model effects. This one-of-a-kind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra. The author begins with a presentation of the classic fixed-effects linear model and goes on to illustrate eight common linear models, along with the value of their use in statistics. From this foundation, subsequent chapters introduce concepts pertaining to the linear model, starting with vector space theory and the theory of least-squares estimation. An outline of the Helmert matrix is also presented, along with a thorough explanation of how the ANOVA is created in both typical two-way and higher layout designs, ultimately revealing the distribution theory. Other important topics covered include: Vector space theory The theory of least squares estimation Gauss-Markov theorem Kronecker products Diagnostic and robust methods for linear models Likelihood approaches to estimation A discussion of Bayesian theory is also included for purposes of comparison and contrast, and numerous illustrative exercises assist the reader with uncovering the nature of the models, using both classic and new data sets. Requiring only a working knowledge of basic probability and statistical inference, Linear Models is a valuable book for courses on linear models at the upper-undergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture.
A First Course In Linear Model Theory
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Author : Nalini Ravishanker
language : en
Publisher: CRC Press
Release Date : 2001-12-21
A First Course In Linear Model Theory written by Nalini Ravishanker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-21 with Mathematics categories.
This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
Advanced Linear Models
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Author : Shein-Chung Chow
language : en
Publisher: CRC Press
Release Date : 1993-12-14
Advanced Linear Models written by Shein-Chung Chow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-14 with Mathematics categories.
This work details the statistical inference of linear models including parameter estimation, hypothesis testing, confidence intervals, and prediction. The authors discuss the application of statistical theories and methodologies to various linear models such as the linear regression model, the analysis of variance model, the analysis of covariance model, and the variance components model.
Visualizing Linear Models
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Author : W. D. Brinda
language : en
Publisher: Springer Nature
Release Date : 2021-02-24
Visualizing Linear Models written by W. D. Brinda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-24 with Mathematics categories.
This book provides a visual and intuitive coverage of the core theory of linear models. Designed to develop fluency with the underlying mathematics and to build a deep understanding of the principles, it's an excellent basis for a one-semester course on statistical theory and linear modeling for intermediate undergraduates or graduate students. Three chapters gradually develop the essentials of linear model theory. They are each preceded by a review chapter that covers a foundational prerequisite topic. This classroom-tested work explores two distinct and complementary types of visualization: the “observations picture” and the “variables picture.” To improve retention of material, this book is supplemented by a bank of ready-made practice exercises for students. These are available for digital or print use.
A First Course In Linear Model Theory
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Author : Nalini Ravishanker
language : en
Publisher: CRC Press
Release Date : 2020-09-14
A First Course In Linear Model Theory written by Nalini Ravishanker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-14 with Mathematics categories.
This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation
Linear Models And Generalizations
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Author : C. Radhakrishna Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-15
Linear Models And Generalizations written by C. Radhakrishna Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-15 with Mathematics categories.
Thebookisbasedonseveralyearsofexperienceofbothauthorsinteaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and o?ers a selectionofclassicalandmodernalgebraicresultsthatareusefulinresearch work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss fu- tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and a variety of practical applications will be useful not only to students but also to researchers and consultants in statistics.