Linear Model Theory

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Linear Models in Statistics

Alvin C. Rencher,G. Bruce Schaalje
Linear Models in Statistics Book PDF

Author : Alvin C. Rencher,G. Bruce Schaalje
Publisher : John Wiley & Sons
Page : 690 pages
File Size : 50,7 Mb
Release : 2008-01-07
Category : Mathematics
ISBN : 9780470192603

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Linear Models in Statistics by Alvin C. Rencher,G. Bruce Schaalje Pdf

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

Dale L. Zimmerman
Linear Model Theory Book PDF

Author : Dale L. Zimmerman
Publisher : Springer Nature
Page : 504 pages
File Size : 48,9 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9783030520632

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Linear Model Theory by Dale L. Zimmerman Pdf

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

Nalini Ravishanker,Dipak K. Dey
A First Course in Linear Model Theory Book PDF

Author : Nalini Ravishanker,Dipak K. Dey
Publisher : CRC Press
Page : 494 pages
File Size : 49,6 Mb
Release : 2001-12-21
Category : Mathematics
ISBN : 1584882476

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A First Course in Linear Model Theory by Nalini Ravishanker,Dipak K. Dey Pdf

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

Brenton R. Clarke
Linear Models Book PDF

Author : Brenton R. Clarke
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 51,8 Mb
Release : 2008-09-19
Category : Mathematics
ISBN : 0470377976

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Linear Models by Brenton R. Clarke Pdf

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.

The Linear Model and Hypothesis

George Seber
The Linear Model and Hypothesis Book PDF

Author : George Seber
Publisher : Springer
Page : 208 pages
File Size : 52,9 Mb
Release : 2015-10-08
Category : Mathematics
ISBN : 9783319219301

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The Linear Model and Hypothesis by George Seber Pdf

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

Shein-Chung Chow
Advanced Linear Models Book PDF

Author : Shein-Chung Chow
Publisher : Routledge
Page : 552 pages
File Size : 45,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351468565

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Advanced Linear Models by Shein-Chung Chow Pdf

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.

Theory of Linear Models

Bent Jorgensen
Theory of Linear Models Book PDF

Author : Bent Jorgensen
Publisher : Routledge
Page : 185 pages
File Size : 46,9 Mb
Release : 2019-01-14
Category : Mathematics
ISBN : 9781351408615

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Theory of Linear Models by Bent Jorgensen Pdf

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 Model Theory

Keith E. Muller,Paul W. Stewart
Linear Model Theory Book PDF

Author : Keith E. Muller,Paul W. Stewart
Publisher : John Wiley & Sons
Page : 427 pages
File Size : 48,7 Mb
Release : 2006-10-06
Category : Mathematics
ISBN : 9780470052136

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Linear Model Theory by Keith E. Muller,Paul W. Stewart Pdf

A precise and accessible presentation of linear model theory, illustrated with data examples Statisticians often use linear models for data analysis and for developing new statistical methods. Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas Linear Model Theory: Univariate, Multivariate, and Mixed Models presents a unified treatment in order to make clear the distinctions among the three classes of models. Linear Model Theory: Univariate, Multivariate, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. Data examples motivate and illustrate the models. Chapters 7-10 address distribution theory of multivariate Gaussian variables and quadratic forms. Chapters 11-19 detail methods for estimation, hypothesis testing, and confidence intervals. The final chapters, 20-23, concentrate on choosing a sample size. Substantial sets of excercises of varying difficulty serve instructors for their classes, as well as help students to test their own knowledge. The reader needs a basic knowledge of statistics, probability, and inference, as well as a solid background in matrix theory and applied univariate linear models from a matrix perspective. Topics covered include: A review of matrix algebra for linear models The general linear univariate model The general linear multivariate model Generalizations of the multivariate linear model The linear mixed model Multivariate distribution theory Estimation in linear models Tests in Gaussian linear models Choosing a sample size in Gaussian linear models Filling the need for a text that provides the necessary theoretical foundations for applying a wide range of methods in real situations, Linear Model Theory: Univariate, Multivariate, and Mixed Models centers on linear models of interval scale responses with finite second moments. Models with complex predictors, complex responses, or both, motivate the presentation.

Linear Regression Analysis

Xin Yan,Xiaogang Su
Linear Regression Analysis Book PDF

Author : Xin Yan,Xiaogang Su
Publisher : World Scientific
Page : 349 pages
File Size : 46,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812834102

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Linear Regression Analysis by Xin Yan,Xiaogang Su Pdf

"This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.

A First Course in Linear Model Theory

Nalini Ravishanker,Dipak K. Dey
A First Course in Linear Model Theory Book PDF

Author : Nalini Ravishanker,Dipak K. Dey
Publisher : CRC Press
Page : 490 pages
File Size : 49,8 Mb
Release : 2020-09-14
Category : Mathematics
ISBN : 9781000228632

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A First Course in Linear Model Theory by Nalini Ravishanker,Dipak K. Dey Pdf

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

C. Radhakrishna Rao,Helge Toutenburg,Shalabh,Christian Heumann
Linear Models and Generalizations Book PDF

Author : C. Radhakrishna Rao,Helge Toutenburg,Shalabh,Christian Heumann
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 55,7 Mb
Release : 2007-10-15
Category : Mathematics
ISBN : 9783540742272

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Linear Models and Generalizations by C. Radhakrishna Rao,Helge Toutenburg,Shalabh,Christian Heumann Pdf

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

P. McCullagh
Generalized Linear Models Book PDF

Author : P. McCullagh
Publisher : Routledge
Page : 361 pages
File Size : 46,7 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351445849

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Generalized Linear Models by P. McCullagh Pdf

The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and ot

Beyond Multiple Linear Regression

Paul Roback,Julie Legler
Beyond Multiple Linear Regression Book PDF

Author : Paul Roback,Julie Legler
Publisher : CRC Press
Page : 436 pages
File Size : 55,9 Mb
Release : 2021-01-14
Category : Mathematics
ISBN : 9781439885406

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Beyond Multiple Linear Regression by Paul Roback,Julie Legler Pdf

Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner. The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling. A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR)

Linear Model Methodology

Andre I. Khuri
Linear Model Methodology Book PDF

Author : Andre I. Khuri
Publisher : CRC Press
Page : 562 pages
File Size : 48,6 Mb
Release : 2009-10-21
Category : Mathematics
ISBN : 9781420010442

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Linear Model Methodology by Andre I. Khuri Pdf

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

Theory and Application of the Linear Model

Franklin A. Graybill
Theory and Application of the Linear Model Book PDF

Author : Franklin A. Graybill
Publisher : Brooks/Cole
Page : 724 pages
File Size : 47,6 Mb
Release : 2000
Category : Analysis of variance
ISBN : UCSC:32106015712398

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Theory and Application of the Linear Model by Franklin A. Graybill Pdf

In THEORY AND APPLICATION OF THE LINEAR MODEL, Franklin A. Graybill integrates the linear statistical model within the context of analysis of variance, correlation and regression, and design of experiments. With topics motivated by real situations, it is a time tested, authoritative resource for experimenters, statistical consultants, and students.