Download or read book Matrix Tricks for Linear Statistical Models written by Simo Puntanen and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.
Download or read book Matrix Tricks for Linear Statistical Models written by Simo Puntanen and published by . This book was released on 2003 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matrix Tricks for Linear Statistical Models written by Jarkko Isotalo and published by . This book was released on 2005 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Matrix Algebra for Linear Models written by Marvin H. J. Gruber and published by John Wiley & Sons. This book was released on 2013-12-31 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
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.
Download or read book Matrix Algebra and Its Applications to Statistics and Econometrics written by Calyampudi Radhakrishna Rao and published by World Scientific. This book was released on 1998 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: "I recommend this book for its extensive coverage of topics not easily found elsewhere and for its focus on applications".Zentralblatt MATH"The book is an excellent source on linear algebra, matrix theory and applications in statistics and econometrics, and is unique in many ways. I recommend it to anyone interested in these disciplines, and especially in how they benefit from one another".Statistical Papers, 2000
Download or read book Basics of Matrix Algebra for Statistics with R written by Nick Fieller and published by CRC Press. This book was released on 2018-09-03 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.
Download or read book Data Analysis Using Regression and Multilevel Hierarchical Models written by Andrew Gelman and published by Cambridge University Press. This book was released on 2007 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2007, is for the applied researcher performing data analysis using linear and nonlinear regression and multilevel models.
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.
Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
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.
Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Download or read book R for Data Science written by Hadley Wickham and published by "O'Reilly Media, Inc.". This book was released on 2016-12-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you've learned along the way. You'll learn how to: Wrangle—transform your datasets into a form convenient for analysis Program—learn powerful R tools for solving data problems with greater clarity and ease Explore—examine your data, generate hypotheses, and quickly test them Model—provide a low-dimensional summary that captures true "signals" in your dataset Communicate—learn R Markdown for integrating prose, code, and results
Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Download or read book Linear Algebra and Optimization for Machine Learning written by Charu C. Aggarwal and published by Springer Nature. This book was released on 2020-05-13 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.
Download or read book Matrix Algebra From a Statistician s Perspective written by David A. Harville and published by Springer Science & Business Media. This book was released on 2008-06-27 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."
