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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: 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: 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: 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: Simon Wood
Publisher: CRC Press
ISBN: 1584884746
Category : Mathematics
Languages : en
Pages : 412
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Book Description
Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.
Author: Stephen L. Campbell
Publisher: SIAM
ISBN: 0898716713
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.
Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477
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Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Rolf Isermann
Publisher: Springer Science & Business Media
ISBN: 3540788794
Category : Technology & Engineering
Languages : en
Pages : 705
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Book Description
Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.
Author: Griffith, Daniel A.
Publisher: Edward Elgar Publishing
ISBN: 1800372825
Category : Social Science
Languages : en
Pages : 125
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Book Description
This Advanced Introduction provides a critical review and discussion of research concerning spatial statistics, differentiating between it and spatial econometrics, to answer a set of core questions covering the geographic-tagging-of-data origins of the concept and its theoretical underpinnings, conceptual advances, and challenges for future scholarly work. It offers a vital tool for understanding spatial statistics and surveys how concerns about violating the independent observations assumption of statistical analysis developed into this discipline.
Author: Christian Barillot
Publisher: Springer
ISBN: 3540301356
Category : Medical
Languages : en
Pages : 967
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Book Description
The 7th International Conference on Medical Imaging and Computer Assisted Intervention, MICCAI 2004, was held in Saint-Malo, Brittany, France at the “Palais du Grand Large” conference center, September 26–29, 2004. The p- posaltohostMICCAI2004wasstronglyencouragedandsupportedbyIRISA, Rennes. IRISA is a publicly funded national research laboratory with a sta? of 370,including150full-timeresearchscientistsorteachingresearchscientistsand 115 postgraduate students. INRIA, the CNRS, and the University of Rennes 1 are all partners in this mixed research unit, and all three organizations were helpful in supporting MICCAI. MICCAI has become a premier international conference with in-depth - pers on the multidisciplinary ?elds of medical image computing, comput- assisted intervention and medical robotics. The conference brings together cl- icians, biological scientists, computer scientists, engineers, physicists and other researchers and o?ers them a forum to exchange ideas in these exciting and rapidly growing ?elds. The impact of MICCAI increases each year and the quality and quantity of submitted papers this year was very impressive. We received a record 516 full submissions (8 pages in length) and 101 short communications (2 pages) from 36 di?erent countries and 5 continents (see ?gures below). All submissions were reviewed by up to 4 external reviewers from the Scienti?c Review C- mittee and a primary reviewer from the Program Committee. All reviews were then considered by the MICCAI 2004 Program Committee, resulting in the acceptance of 235 full papers and 33 short communications.
