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A Comparison Of Mixed And Minimax Estimators Of Linear Models
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Book Synopsis Regression Estimators by : Marvin H. J. Gruber
Download or read book Regression Estimators written by Marvin H. J. Gruber and published by Academic Press. This book was released on 2014-05-10 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression Estimators: A Comparative Study presents, compares, and contrasts the development and the properties of the ridge type estimators that result from both Bayesian and non-Bayesian (frequentist) methods. The book is divided into four parts. The first part (Chapters I and II) discusses the need for alternatives to least square estimators, gives a historical survey of the literature and summarizes basic ideas in Matrix Theory and Statistical Decision Theory used throughout the book. The second part (Chapters III and IV) covers the estimators from both the Bayesian and from the frequentist points of view and explores the mathematical relationships between them. The third part (Chapters V-VIII) considers the efficiency of the estimators with and without averaging over a prior distribution. Part IV, the final two chapters IX and X, suggests applications of the methods and results of Chapters III-VII to Kaiman Filters and Analysis of Variance, two very important areas of application. Statisticians and workers in fields that use statistical methods who would like to know more about the analytical properties of ridge type estimators will find the book invaluable.
Book Synopsis Improving Efficiency by Shrinkage by : Marvin Gruber
Download or read book Improving Efficiency by Shrinkage written by Marvin Gruber and published by Routledge. This book was released on 2017-11-01 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a treatment of different kinds of James-Stein and ridge regression estimators from a frequentist and Bayesian point of view. The book explains and compares estimators analytically as well as numerically and includes Mathematica and Maple programs used in numerical comparison.;College or university bookshops may order five or more copies at a special student rate, available on request.
Book Synopsis Matrix Algebra for Linear Models by : Marvin H. J. Gruber
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.
Book Synopsis Linear Models by : Calyampudi R. Rao
Download or read book Linear Models written by Calyampudi R. Rao and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of the theory and applications of linear models, for use as a textbook in statistics at graduate level as well as an accompanying text for other courses in which linear models play a part. The authors present a unified theory of inference from linear models with minimal assumptions, not only through least squares theory, but also using alternative methods of estimation and testing based on convex loss functions and general estimating equations. Highlights include: - a special emphasis on sensitivity analysis and model selection; - a chapter devoted to the analysis of categorical data based on logic, loglinear, and logistic regression models; - a chapter devoted to incomplete data sets; - an extensive appendix on matrix theory; - a chapter devoted to the analysis of categorical data based on a unified presentation of generalized linear models including GEE-methods for correlated response; - a chapter devoted to incomplete data sets including regression diagnostics to identify Non-MCAR-processes The material covered is thus invaluable not only to graduates, but also to researchers and consultants in statistics.
Book Synopsis Time Series and Econometric Modelling by : I.B. MacNeill
Download or read book Time Series and Econometric Modelling written by I.B. MacNeill and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: On May 27-31, 1985, a series of symposia was held at The University of Western Ontario, London, Canada, to celebrate the 70th birthday of Pro fessor V. M. Joshi. These symposia were chosen to reflect Professor Joshi's research interests as well as areas of expertise in statistical science among faculty in the Departments of Statistical and Actuarial Sciences, Economics, Epidemiology and Biostatistics, and Philosophy. From these symposia, the six volumes which comprise the "Joshi Festschrift" have arisen. The 117 articles in this work reflect the broad interests and high quality of research of those who attended our conference. We would like to thank all of the contributors for their superb cooperation in helping us to complete this project. Our deepest gratitude must go to the three people who have spent so much of their time in the past year typing these volumes: Jackie Bell, Lise Constant, and Sandy Tarnowski. This work has been printed from "camera ready" copy produced by our Vax 785 computer and QMS Lasergraphix printers, using the text processing software TEX. At the initiation of this project, we were neophytes in the use of this system. Thank you, Jackie, Lise, and Sandy, for having the persistence and dedication needed to complete this undertaking.
Book Synopsis Linear Models by : C.Radhakrishna Rao
Download or read book Linear Models written by C.Radhakrishna Rao and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on both authors' several years of experience in teaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results about the definiteness of matrices, especially for the differences of matrices, which enable superiority comparisons of two biased estimates to be made for the first time. We have attempted to provide a unified theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss func tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and its practical applica tions will be useful not only to students but also to researchers and con sultants in statistics.
Book Synopsis Statistical Theory and Method Abstracts by :
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 1998 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Models and Generalizations by : C. Radhakrishna Rao
Download or read book Linear Models and Generalizations written by C. Radhakrishna Rao and published by Springer Science & Business Media. This book was released on 2007-10-15 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Prior Information in Linear Models by : Helge Toutenburg
Download or read book Prior Information in Linear Models written by Helge Toutenburg and published by John Wiley & Sons. This book was released on 1982 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The University of Western Ontario Series in Philosophy of Science by :
Download or read book The University of Western Ontario Series in Philosophy of Science written by and published by . This book was released on 1987 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research in Progress written by and published by . This book was released on 1967 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the International Conference on Linear Statistical Inference LINSTAT ’93 by : Tadeusz Calinski
Download or read book Proceedings of the International Conference on Linear Statistical Inference LINSTAT ’93 written by Tadeusz Calinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Linear Statistical Inference LINSTAT'93 was held in Poznan, Poland, from May 31 to June 4, 1993. The purpose of the confer ence was to enable scientists, from various countries, engaged in the diverse areas of statistical sciences and practice to meet together and exchange views and re sults related to the current research on linear statistical inference in its broadest sense. Thus, the conference programme included sessions on estimation, prediction and testing in linear models, on robustness of some relevant statistical methods, on estimation of variance components appearing in linear models, on certain gen eralizations to nonlinear models, on design and analysis of experiments, including optimality and comparison of linear experiments, and on some other topics related to linear statistical inference. Within the various sessions 22 invited papers and 37 contributed papers were presented, 12 of them as posters. The conference gathered 94 participants from eighteen countries of Europe, North America and Asia. There were 53 participants from abroad and 41 from Poland. The conference was the second of this type, devoted to linear statistical inference. The first was held in Poznan in June, 4-8, 1984. Both belong to the series of confer ences on mathematical statistics and probability theory organized under the auspices of the Committee of Mathematics of the Polish Academy of Sciences, due to the ini tiative and efforts of its Mathematical Statistics Section. In the years 1973-1993 there were held in Poland nineteen such conferences, some of them international.
Book Synopsis Applications of Linear and Nonlinear Models by : Erik Grafarend
Download or read book Applications of Linear and Nonlinear Models written by Erik Grafarend and published by Springer Science & Business Media. This book was released on 2012-08-15 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 1368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sample Surveys: Inference and Analysis by :
Download or read book Sample Surveys: Inference and Analysis written by and published by Morgan Kaufmann. This book was released on 2009-09-02 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Statistics_29B contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications. Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 1 deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 2 is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects. - Comprehensive account of recent developments in sample survey theory and practice - Covers a wide variety of diverse applications - Comprehensive bibliography
Book Synopsis Stochastic Orders and Applications by : Karl Mosler
Download or read book Stochastic Orders and Applications written by Karl Mosler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.
Author :American Statistical Association. Business and Economic Statistics Section Publisher : ISBN 13 : Total Pages :804 pages Book Rating :4.E/5 ( download)
Book Synopsis Proceedings of the Business and Economic Statistics Section by : American Statistical Association. Business and Economic Statistics Section
Download or read book Proceedings of the Business and Economic Statistics Section written by American Statistical Association. Business and Economic Statistics Section and published by . This book was released on 1983 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
