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Author: George Arthur Frederick Seber
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 132
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Book Description
Author: George Arthur Frederick Seber
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 132
Get Book Here
Book Description
Author: George Arthur Frederick Seber
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages :
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Book Description
Author: George Seber
Publisher: Springer
ISBN: 3319219308
Category : Mathematics
Languages : en
Pages : 208
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Book Description
This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involvematrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.
Author: George A. F. Seber
Publisher: John Wiley & Sons
ISBN: 1118274423
Category : Mathematics
Languages : en
Pages : 584
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Book Description
Concise, mathematically clear, and comprehensive treatment of the subject. * Expanded coverage of diagnostics and methods of model fitting. * Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models. * More than 200 problems throughout the book plus outline solutions for the exercises. * This revision has been extensively class-tested.
Author: Ronald Christensen
Publisher: Springer Nature
ISBN: 3030320979
Category : Mathematics
Languages : en
Pages : 539
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Book Description
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.
Author: Maxwell L. King
Publisher: Routledge
ISBN: 1351140663
Category : Business & Economics
Languages : en
Pages : 550
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Book Description
Originally published in 1987. This collection of original papers deals with various issues of specification in the context of the linear statistical model. The volume honours the early econometric work of Donald Cochrane, late Dean of Economics and Politics at Monash University in Australia. The chapters focus on problems associated with autocorrelation of the error term in the linear regression model and include appraisals of early work on this topic by Cochrane and Orcutt. The book includes an extensive survey of autocorrelation tests; some exact finite-sample tests; and some issues in preliminary test estimation. A wide range of other specification issues is discussed, including the implications of random regressors for Bayesian prediction; modelling with joint conditional probability functions; and results from duality theory. There is a major survey chapter dealing with specification tests for non-nested models, and some of the applications discussed by the contributors deal with the British National Accounts and with Australian financial and housing markets.
Author: George A. F. Seber
Publisher: John Wiley & Sons
ISBN: 0470226781
Category : Mathematics
Languages : en
Pages : 592
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Book Description
A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: Complex matrices A wide range of special matrices and their properties Special products and operators, such as the Kronecker product Partitioned and patterned matrices Matrix analysis and approximation Matrix optimization Majorization Random vectors and matrices Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.
Author: James H. Stapleton
Publisher: John Wiley & Sons
ISBN: 0470317760
Category : Mathematics
Languages : en
Pages : 474
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Book Description
Linear Statistical Models Developed and refined over a period of twenty years, the material in this book offers an especially lucid presentation of linear statistical models. These models lead to what is usually called "multiple regression" or "analysis of variance" methodology, which, in turn, opens up a wide range of applications to the physical, biological, and social sciences, as well as to business, agriculture, and engineering. Unlike similar books on this topic, Linear Statistical Models emphasizes the geometry of vector spaces because of the intuitive insights this approach brings to an understanding of the theory. While the focus is on theory, examples of applications, using the SAS and S-Plus packages, are included. Prerequisites include some familiarity with linear algebra, and probability and statistics at the postcalculus level. Major topics covered include: * Methods of study of random vectors, including the multivariate normal, chi-square, t and F distributions, central and noncentral * The linear model and the basic theory of regression analysis and the analysis of variance * Multiple regression methods, including transformations, analysis of residuals, and asymptotic theory for regression analysis. Separate sections are devoted to robust methods and to the bootstrap. * Simultaneous confidence intervals: Bonferroni, Scheffe, Tukey, and Bechhofer * Analysis of variance, with two- and three-way analysis of variance * Random component models, nested designs, and balanced incomplete block designs * Analysis of frequency data through log-linear models, with emphasis on vector space viewpoint. This chapter alone is sufficient for a course on the analysis of frequency data.
Author: Alexander Basilevsky
Publisher: Courier Corporation
ISBN: 0486153371
Category : Mathematics
Languages : en
Pages : 412
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Book Description
This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.
Author: Raimund Alt
Publisher: Cuvillier Verlag
ISBN: 3865373380
Category :
Languages : en
Pages : 141
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Book Description
