A First Course In The Theory Of Linear Statistical Models
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| Author | : Nalini Ravishanker |
| Publisher | : CRC Press |
| Total Pages | : 494 |
| Release | : 2001-12-21 |
| Genre | : Mathematics |
| ISBN | : 9781584882473 |
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.
| Author | : Janet Susan Milton |
| Publisher | : McGraw-Hill Primis Custom Pub |
| Total Pages | : 350 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780072327083 |
This is a teaching text for the advanced statistics undergraduate or the beginning graduate student of statistics. It is assumed that the user of the text has had at least a full year course in applied or mathematical statistics. The text is intended for a one semester introductory course in the theory of linear statistical models.
| Author | : James H. Stapleton |
| Publisher | : John Wiley & Sons |
| Total Pages | : 517 |
| Release | : 2009-08-03 |
| Genre | : Mathematics |
| ISBN | : 0470231467 |
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.
| Author | : Alvin C. Rencher |
| Publisher | : John Wiley & Sons |
| Total Pages | : 690 |
| Release | : 2008-01-07 |
| Genre | : Mathematics |
| ISBN | : 0470192607 |
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.
| Author | : Dale L. Zimmerman |
| Publisher | : Springer Nature |
| Total Pages | : 504 |
| Release | : 2020-11-02 |
| Genre | : Mathematics |
| ISBN | : 3030520633 |
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.
| Author | : John F. Monahan |
| Publisher | : CRC Press |
| Total Pages | : 292 |
| Release | : 2008-03-31 |
| Genre | : Mathematics |
| ISBN | : 1420062042 |
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.
| Author | : John H. Skillings |
| Publisher | : CRC Press |
| Total Pages | : 700 |
| Release | : 1999-11-24 |
| Genre | : Mathematics |
| ISBN | : 9780849396717 |
Most texts on experimental design fall into one of two distinct categories. There are theoretical works with few applications and minimal discussion on design, and there are methods books with limited or no discussion of the underlying theory. Furthermore, most of these tend to either treat the analysis of each design separately with little attempt to unify procedures, or they will integrate the analysis for the designs into one general technique. A First Course in the Design of Experiments: A Linear Models Approach stands apart. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. The authors begin with a general introduction then lead students through the theoretical results, the various design models, and the analytical concepts that will enable them to analyze virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. The authors use the SAS software package throughout the book, but also demonstrate how any regression program can be used for analysis. With its balanced presentation of theory, methods, and applications and its highly readable style, A First Course in the Design of Experiments proves ideal as a text for a beginning graduate or upper-level undergraduate course in the design and analysis of experiments.
| Author | : David A. Freedman |
| Publisher | : Cambridge University Press |
| Total Pages | : 459 |
| Release | : 2009-04-27 |
| Genre | : Mathematics |
| ISBN | : 1139477315 |
This lively and engaging book explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modelling, and the pitfalls. The discussion shows you how to think about the critical issues - including the connection (or lack of it) between the statistical models and the real phenomena. The book is written for advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences.
| Author | : Alan Agresti |
| Publisher | : John Wiley & Sons |
| Total Pages | : 471 |
| Release | : 2015-02-23 |
| Genre | : Mathematics |
| ISBN | : 1118730038 |
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.
| Author | : Michael H. Kutner |
| Publisher | : McGraw-Hill/Irwin |
| Total Pages | : 701 |
| Release | : 2003-09 |
| Genre | : Mathematics |
| ISBN | : 9780072955675 |
Kutner, Neter, Nachtsheim, Wasserman, Applied Linear Regression Models, 4/e (ALRM4e) is the long established leading authoritative text and reference on regression (previously Neter was lead author.) For students in most any discipline where statistical analysis or interpretation is used, ALRM has served as the industry standard. The text includes brief introductory and review material, and then proceeds through regression and modeling. All topics are presented in a precise and clear style supported with solved examples, numbered formulae, graphic illustrations, and "Notes" to provide depth and statistical accuracy and precision. Applications used within the text and the hallmark problems, exercises, and projects are drawn from virtually all disciplines and fields providing motivation for students in any discipline. ALRM 4e provides an increased use of computing and graphical analysis throughout, without sacrificing concepts or rigor by using larger data sets in examples and exercises, and where methods can be automated within software without loss of understanding, it is so done.
