Theory Of Linear Models

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Linear Models in Statistics

Author : Alvin C. Rencher
Publisher : John Wiley & Sons
ISBN 13 : 0470192607
Total Pages : 690 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Linear Models in Statistics by : Alvin C. Rencher

Download or read book Linear Models in Statistics written by Alvin C. Rencher and published by John Wiley & Sons. This book was released on 2008-01-07 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Model Theory

Author : Dale L. Zimmerman
Publisher : Springer Nature
ISBN 13 : 3030520633
Total Pages : 513 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Linear Model Theory by : Dale L. Zimmerman

Download or read book Linear Model Theory written by Dale L. Zimmerman and published by Springer Nature. This book was released on 2020-11-02 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A First Course in Linear Model Theory

Author : Nalini Ravishanker
Publisher : CRC Press
ISBN 13 : 9781584882473
Total Pages : 494 pages
Book Rating : 4.8/5 (824 download)

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Book Synopsis A First Course in Linear Model Theory by : Nalini Ravishanker

Download or read book A First Course in Linear Model Theory written by Nalini Ravishanker and published by CRC Press. This book was released on 2001-12-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Models

Author : Brenton R. Clarke
Publisher : John Wiley & Sons
ISBN 13 : 9780470377970
Total Pages : 288 pages
Book Rating : 4.3/5 (779 download)

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Book Synopsis Linear Models by : Brenton R. Clarke

Download or read book Linear Models written by Brenton R. Clarke and published by John Wiley & Sons. This book was released on 2008-09-19 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Linear Models

Author : Bent Jorgensen
Publisher : Routledge
ISBN 13 : 1351408615
Total Pages : 244 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Theory of Linear Models by : Bent Jorgensen

Download or read book Theory of Linear Models written by Bent Jorgensen and published by Routledge. This book was released on 2019-01-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Plane Answers to Complex Questions

Author : Ronald Christensen
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 480 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Plane Answers to Complex Questions by : Ronald Christensen

Download or read book Plane Answers to Complex Questions written by Ronald Christensen and published by Springer Science & Business Media. This book was released on 1996 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 with R

Author : Julian J. Faraway
Publisher : CRC Press
ISBN 13 : 1439887349
Total Pages : 284 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Linear Models with R by : Julian J. Faraway

Download or read book Linear Models with R written by Julian J. Faraway and published by CRC Press. This book was released on 2016-04-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models

The Linear Model and Hypothesis

Author : George Seber
Publisher : Springer
ISBN 13 : 3319219308
Total Pages : 208 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis The Linear Model and Hypothesis by : George Seber

Download or read book The Linear Model and Hypothesis written by George Seber and published by Springer. This book was released on 2015-10-08 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Shein-Chung Chow
Publisher : Routledge
ISBN 13 : 1351468561
Total Pages : 556 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Advanced Linear Models by : Shein-Chung Chow

Download or read book Advanced Linear Models written by Shein-Chung Chow and published by Routledge. This book was released on 2018-05-04 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Andre I. Khuri
Publisher : CRC Press
ISBN 13 : 1420010441
Total Pages : 562 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Linear Model Methodology by : Andre I. Khuri

Download or read book Linear Model Methodology written by Andre I. Khuri and published by CRC Press. This book was released on 2009-10-21 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Foundations of Linear and Generalized Linear Models

Author : Alan Agresti
Publisher : John Wiley & Sons
ISBN 13 : 1118730038
Total Pages : 471 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Foundations of Linear and Generalized Linear Models by : Alan Agresti

Download or read book Foundations of Linear and Generalized Linear Models written by Alan Agresti and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.

Linear Statistical Models

Author : James H. Stapleton
Publisher : John Wiley & Sons
ISBN 13 : 0470231467
Total Pages : 517 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis Linear Statistical Models by : James H. Stapleton

Download or read book Linear Statistical Models written by James H. Stapleton and published by John Wiley & Sons. This book was released on 2009-08-03 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "This impressive and eminently readable text . . . [is] a welcome addition to the statistical literature." —The Indian Journal of Statistics Revised to reflect the current developments on the topic, Linear Statistical Models, Second Edition provides an up-to-date approach to various statistical model concepts. The book includes clear discussions that illustrate key concepts in an accessible and interesting format while incorporating the most modern software applications. This Second Edition follows an introduction-theorem-proof-examples format that allows for easier comprehension of how to use the methods and recognize the associated assumptions and limits. In addition to discussions on the methods of random vectors, multiple regression techniques, simultaneous confidence intervals, and analysis of frequency data, new topics such as mixed models and curve fitting of models have been added to thoroughly update and modernize the book. Additional topical coverage includes: An introduction to R and S-Plus® with many examples Multiple comparison procedures Estimation of quantiles for regression models An emphasis on vector spaces and the corresponding geometry Extensive graphical displays accompany the book's updated descriptions and examples, which can be simulated using R, S-Plus®, and SAS® code. Problems at the end of each chapter allow readers to test their understanding of the presented concepts, and additional data sets are available via the book's FTP site. Linear Statistical Models, Second Edition is an excellent book for courses on linear models at the upper-undergraduate and graduate levels. It also serves as a comprehensive reference for statisticians, engineers, and scientists who apply multiple regression or analysis of variance in their everyday work.

A Primer on Linear Models

Author : John F. Monahan
Publisher : CRC Press
ISBN 13 : 1420062042
Total Pages : 292 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis A Primer on Linear Models by : John F. Monahan

Download or read book A Primer on Linear Models written by John F. Monahan and published by CRC Press. This book was released on 2008-03-31 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods.

Regression

Author : N. H. Bingham
Publisher : Springer Science & Business Media
ISBN 13 : 1848829698
Total Pages : 293 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Regression by : N. H. Bingham

Download or read book Regression written by N. H. Bingham and published by Springer Science & Business Media. This book was released on 2010-09-17 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential. Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions. The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh’s Probability Models, and T. S. Blyth & E.F. Robertsons’ Basic Linear Algebra and Further Linear Algebra.

Linear Algebra and Linear Models

Author : Ravindra B. Bapat
Publisher : Springer Science & Business Media
ISBN 13 : 038722601X
Total Pages : 145 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Linear Algebra and Linear Models by : Ravindra B. Bapat

Download or read book Linear Algebra and Linear Models written by Ravindra B. Bapat and published by Springer Science & Business Media. This book was released on 2008-01-18 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians.

Linear Models and Generalizations

Author : C. Radhakrishna Rao
Publisher : Springer Science & Business Media
ISBN 13 : 3540742271
Total Pages : 583 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Linear Models and Generalizations by : C. Radhakrishna Rao

Download or read book Linear Models and Generalizations written by C. Radhakrishna Rao and published by Springer Science & Business Media. This book was released on 2007-10-15 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated with the latest results, this Third Edition explores the theory and applications of linear models. The authors present a unified theory of inference from linear models and its generalizations with minimal assumptions. They not only use least squares theory, but also alternative methods of estimation and testing based on convex loss functions and general estimating equations. Highlights of coverage include sensitivity analysis and model selection, an analysis of incomplete data, an analysis of categorical data based on a unified presentation of generalized linear models, and an extensive appendix on matrix theory.

Generalized Linear Models With Examples in R

Author : Peter K. Dunn
Publisher : Springer
ISBN 13 : 1441901183
Total Pages : 573 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Generalized Linear Models With Examples in R by : Peter K. Dunn

Download or read book Generalized Linear Models With Examples in R written by Peter K. Dunn and published by Springer. This book was released on 2018-11-10 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an introduction to generalized linear models, complete with real-world data sets and practice problems, making it applicable for both beginning and advanced students of applied statistics. Generalized linear models (GLMs) are powerful tools in applied statistics that extend the ideas of multiple linear regression and analysis of variance to include response variables that are not normally distributed. As such, GLMs can model a wide variety of data types including counts, proportions, and binary outcomes or positive quantities. The book is designed with the student in mind, making it suitable for self-study or a structured course. Beginning with an introduction to linear regression, the book also devotes time to advanced topics not typically included in introductory textbooks. It features chapter introductions and summaries, clear examples, and many practice problems, all carefully designed to balance theory and practice. The text also provides a working knowledge of applied statistical practice through the extensive use of R, which is integrated into the text. Other features include: • Advanced topics such as power variance functions, saddlepoint approximations, likelihood score tests, modified profile likelihood, small-dispersion asymptotics, and randomized quantile residuals • Nearly 100 data sets in the companion R package GLMsData • Examples that are cross-referenced to the companion data set, allowing readers to load the data and follow the analysis in their own R session