Theory Of Linear Models
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Theory Of Linear Models
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Author : Bent Jorgensen
language : en
Publisher: Routledge
Release Date : 2019-01-14
Theory Of Linear Models written by Bent Jorgensen and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-14 with Mathematics categories.
Providing a self-contained exposition of the theory of linear models, this treatise strikes a compromise between theory and practice, providing a sound theoretical basis while putting the theory to work in important cases.
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.
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
The Theory Of Linear Models And Multivariate Analysis
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Author : Steven F. Arnold
language : en
Publisher: John Wiley & Sons
Release Date : 1981
The Theory Of Linear Models And Multivariate Analysis written by Steven F. Arnold 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 1981 with Mathematics categories.
Basic statistical definitions and theorems. Subspaces and projections. Properties of the multivariate and spherical normal distributions. Introduction to linear models. A sufficient statistic. Estimation. Tests about the mean. Simultaneous confidence intervals - scheffe type. Tests about the variance. Asymptotic validity of procedures under nonnormal distributions. James-Stein and Ridge estimators. Inference based on the studentized range distribution and bonferroni's inequality. The generalized linear model. The repeated measures model. Random effects and mixed models. The correlation model. The distribution theory for multivariate analysis. The multivariate one-and two-sample models - inference about the mean vector. The multivariate linear model. Discriminant analysis. Testing hypotheses about the covariance matrix. Simplifying the structure of the covariance matrix.
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
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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.
Plane Answers To Complex Questions
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Author : Ronald Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
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 2013-03-09 with Mathematics categories.
The second edition of Plane Answers has many additions and a couple of deletions. New material includes additional illustrative examples in Ap pendices A and B and Chapters 2 and 3, as well as discussions of Bayesian estimation, near replicate lack of fit tests, testing the independence assump tion, testing variance components, the interblock analysis for balanced in complete block designs, nonestimable constraints, analysis of unreplicated experiments using normal plots, tensors, and properties of Kronecker prod ucts and Vee operators. The book contains an improved discussion of the relation between ANOVA and regression, and an improved presentation of general Gauss-Markov models. The primary material that has been deleted are the discussions of weighted means and of log-linear models. The mate rial on log-linear models was included in Christensen (1990b), so it became redundant here. Generally, I have tried to clean up the presentation of ideas wherever it seemed obscure to me. Much of the work on the second edition was done while on sabbatical at the University of Canterbury in Christchurch, New Zealand. I would par ticularly like to thank John Deely for arranging my sabbatical. Through their comments and criticisms, four people were particularly helpful in con structing this new edition. I would like to thank Wes Johnson, Snehalata Huzurbazar, Ron Butler, and Vance Berger.
The Linear Model And Hypothesis
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Author : George Seber
language : en
Publisher: Springer
Release Date : 2015-10-08
The Linear Model And Hypothesis written by George Seber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.
This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involvematrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.
Advanced Linear Models
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Author : Shein-Chung Chow
language : en
Publisher: Routledge
Release Date : 2018-05-04
Advanced Linear Models written by Shein-Chung Chow and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 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.
Linear Model Methodology
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Author : Andre I. Khuri
language : en
Publisher: CRC Press
Release Date : 2009-10-21
Linear Model Methodology written by Andre I. Khuri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-21 with Mathematics categories.
Given the importance of linear models in statistical theory and experimental research, a good understanding of their fundamental principles and theory is essential. Supported by a large number of examples, Linear Model Methodology provides a strong foundation in the theory of linear models and explores the latest developments in data analysis.After