Generalized Least Squares PDF Download

Author: Takeaki Kariya
Publisher: John Wiley & Sons
ISBN: 0470866985
Category : Mathematics
Languages : en
Pages : 312

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Book Description
Generalised Least Squares adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified theory of generalized least squares estimations, adopting a concise and mathematically rigorous approach. The book covers in depth the 'lower and upper bounds approach', pioneered by the first author, which is widely regarded as a very powerful and useful tool for generalized least squares estimation, helping the reader develop their understanding of the theory. The book also contains exercises at the end of each chapter and applications to statistics, econometrics, and biometrics, enabling use for self-study or as a course text.

Author: László Zsolt Garamszegi
Publisher: Springer
ISBN: 3662435500
Category : Science
Languages : en
Pages : 553

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Book Description
Phylogenetic comparative approaches are powerful analytical tools for making evolutionary inferences from interspecific data and phylogenies. The phylogenetic toolkit available to evolutionary biologists is currently growing at an incredible speed, but most methodological papers are published in the specialized statistical literature and many are incomprehensible for the user community. This textbook provides an overview of several newly developed phylogenetic comparative methods that allow to investigate a broad array of questions on how phenotypic characters evolve along the branches of phylogeny and how such mechanisms shape complex animal communities and interspecific interactions. The individual chapters were written by the leading experts in the field and using a language that is accessible for practicing evolutionary biologists. The authors carefully explain the philosophy behind different methodologies and provide pointers – mostly using a dynamically developing online interface – on how these methods can be implemented in practice. These “conceptual” and “practical” materials are essential for expanding the qualification of both students and scientists, but also offer a valuable resource for educators. Another value of the book are the accompanying online resources (available at: http://www.mpcm-evolution.com), where the authors post and permanently update practical materials to help embed methods into practice.

Author: Thomas B. Fomby
Publisher: Springer Science & Business Media
ISBN: 1441987460
Category : Business & Economics
Languages : en
Pages : 637

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Book Description
This book had its conception in 1975in a friendly tavern near the School of Businessand PublicAdministration at the UniversityofMissouri-Columbia. Two of the authors (Fomby and Hill) were graduate students of the third (Johnson), and were (and are) concerned about teaching econometrics effectively at the graduate level. We decided then to write a book to serve as a comprehensive text for graduate econometrics. Generally, the material included in the bookand itsorganization have been governed by the question, " Howcould the subject be best presented in a graduate class?" For content, this has meant that we have tried to cover " all the bases " and yet have not attempted to be encyclopedic. The intended purpose has also affected the levelofmathematical rigor. We have tended to prove only those results that are basic and/or relatively straightforward. Proofs that would demand inordinant amounts of class time have simply been referenced. The book is intended for a two-semester course and paced to admit more extensive treatment of areas of specific interest to the instructor and students. We have great confidence in the ability, industry, and persistence of graduate students in ferreting out and understanding the omitted proofs and results. In the end, this is how one gains maturity and a fuller appreciation for the subject in any case. It is assumed that the readers of the book will have had an econometric methods course, using texts like J. Johnston's Econometric Methods, 2nd ed.

Author: Damodar N. Gujarati
Publisher: SAGE Publications
ISBN: 1544336551
Category : Social Science
Languages : en
Pages : 282

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Book Description
Damodar N. Gujarati’s Linear Regression: A Mathematical Introduction presents linear regression theory in a rigorous, but approachable manner that is accessible to students in all social sciences. This concise title goes step-by-step through the intricacies, and theory and practice of regression analysis. The technical discussion is provided in a clear style that doesn’t overwhelm the reader with abstract mathematics. End-of-chapter exercises test mastery of the content and advanced discussion of some of the topics is offered in the appendices.

Author: Ake Bjorck
Publisher: SIAM
ISBN: 9781611971484
Category : Mathematics
Languages : en
Pages : 425

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Book Description
The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.

Author: C. Radhakrishna Rao
Publisher: Springer Science & Business Media
ISBN: 3540742271
Category : Mathematics
Languages : en
Pages : 583

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Book Description
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.

Author: Takeshi Amemiya
Publisher: Harvard University Press
ISBN: 9780674005600
Category : Business & Economics
Languages : en
Pages : 540

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Book Description
The main features of this text are a thorough treatment of cross-section models—including qualitative response models, censored and truncated regression models, and Markov and duration models—and a rigorous presentation of large sample theory, classical least-squares and generalized least-squares theory, and nonlinear simultaneous equation models.

Author: Justine Shults
Publisher: CRC Press
ISBN: 1420099930
Category : Mathematics
Languages : en
Pages : 223

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Book Description
Drawing on the authors’ substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression—a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitudinal data, familial data, and data with multiple sources of correlation. In some settings, QLS also allows for improved analysis with an unstructured correlation matrix. Special focus is given to goodness-of-fit analysis as well as new strategies for selecting the appropriate working correlation structure for QLS and GEE. A chapter on longitudinal binary data tackles recent issues raised in the statistical literature regarding the appropriateness of semi-parametric methods, such as GEE and QLS, for the analysis of binary data; this chapter includes a comparison with the first-order Markov maximum-likelihood (MARK1ML) approach for binary data. Examples throughout the book demonstrate each topic of discussion. In particular, a fully worked out example leads readers from model building and interpretation to the planning stages for a future study (including sample size calculations). The code provided enables readers to replicate many of the examples in Stata, often with corresponding R, SAS, or MATLAB® code offered in the text or on the book’s website.

Author: Raymond H. Myers
Publisher: John Wiley & Sons
ISBN: 0470556978
Category : Mathematics
Languages : en
Pages : 521

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Book Description
Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities." —Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the latest developments, relevant computational approaches, and modern examples from the fields of engineering and physical sciences. This new edition maintains its accessible approach to the topic by reviewing the various types of problems that support the use of GLMs and providing an overview of the basic, related concepts such as multiple linear regression, nonlinear regression, least squares, and the maximum likelihood estimation procedure. Incorporating the latest developments, new features of this Second Edition include: A new chapter on random effects and designs for GLMs A thoroughly revised chapter on logistic and Poisson regression, now with additional results on goodness of fit testing, nominal and ordinal responses, and overdispersion A new emphasis on GLM design, with added sections on designs for regression models and optimal designs for nonlinear regression models Expanded discussion of weighted least squares, including examples that illustrate how to estimate the weights Illustrations of R code to perform GLM analysis The authors demonstrate the diverse applications of GLMs through numerous examples, from classical applications in the fields of biology and biopharmaceuticals to more modern examples related to engineering and quality assurance. The Second Edition has been designed to demonstrate the growing computational nature of GLMs, as SAS®, Minitab®, JMP®, and R software packages are used throughout the book to demonstrate fitting and analysis of generalized linear models, perform inference, and conduct diagnostic checking. Numerous figures and screen shots illustrating computer output are provided, and a related FTP site houses supplementary material, including computer commands and additional data sets. Generalized Linear Models, Second Edition is an excellent book for courses on regression analysis and regression modeling at the upper-undergraduate and graduate level. It also serves as a valuable reference for engineers, scientists, and statisticians who must understand and apply GLMs in their work.

Author: Farebrother
Publisher: Routledge
ISBN: 1351435264
Category : Mathematics
Languages : en
Pages : 320

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Book Description
Presenting numerous algorithms in a simple algebraic form so that the reader can easilytranslate them into any computer language, this volume gives details of several methodsfor obtaining accurate least squares estimates. It explains how these estimates may beupdated as new information becomes available and how to test linear hypotheses.Linear Least Squares Computations features many structured exercises that guidethe reader through the available algorithms, plus a glossary of commonly used terms anda bibliography of supplementary reading ... collects "ancient" and modem results onlinear least squares computations in a convenient single source . . . develops the necessarymatrix algebra in the context of multivariate statistics . .. only makes peripheral use ofconcepts such as eigenvalues and partial differentiation .. . interprets canonical formsemployed in computation ... discusses many variants of the Gauss, Laplace-Schmidt,Givens, and Householder algorithms ... and uses an empirical approach for the appraisalof algorithms.Linear Least Squares Computations serves as an outstanding reference forindustrial and applied mathematicians, statisticians, and econometricians, as well as atext for advanced undergraduate and graduate statistics, mathematics, and econometricscourses in computer programming, linear regression analysis, and applied statistics.