Parameter Estimation And Hypothesis Testing In Linear Models

Author : Karl-Rudolf Koch
Publisher : Springer Science & Business Media
ISBN 13 : 3662039761
Total Pages : 344 pages
Book Rating : 4.62/5 ( download)

DOWNLOAD NOW!

Download or read book Parameter Estimation and Hypothesis Testing in Linear Models written by Karl-Rudolf Koch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.

Author : Shein-Chung Chow
Publisher : Routledge
ISBN 13 : 1351468561
Total Pages : 552 pages
Book Rating : 4.65/5 ( download)

DOWNLOAD NOW!

Download or read book Advanced Linear Models written by Shein-Chung Chow and published by Routledge. This book was released on 2018-05-04 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work details the statistical inference of linear models including parameter estimation, hypothesis testing, confidence intervals, and prediction. The authors discuss the application of statistical theories and methodologies to various linear models such as the linear regression model, the analysis of variance model, the analysis of covariance model, and the variance components model.

Author : George Arthur Frederick Seber
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.90/5 ( download)

DOWNLOAD NOW!

Download or read book The Linear Hypothesis written by George Arthur Frederick Seber and published by . This book was released on 1980 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : C. Dubbelman
Publisher : Springer Science & Business Media
ISBN 13 : 1468469568
Total Pages : 116 pages
Book Rating : 4.61/5 ( download)

DOWNLOAD NOW!

Download or read book Disturbances in the linear model, estimation and hypothesis testing written by C. Dubbelman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1. The general linear model All econometric research is based on a set of numerical data relating to certain economic quantities, and makes infer ences from the data about the ways in which these quanti ties are related (Malinvaud 1970, p. 3). The linear relation is frequently encountered in applied econometrics. Let y and x denote two economic quantities, then the linear relation between y and x is formalized by: where {31 and {32 are constants. When {31 and {32 are known numbers, the value of y can be calculated for every given value of x. Here y is the dependent variable and x is the explanatory variable. In practical situations {31 and {32 are unknown. We assume that a set of n observations on y and x is available. When plotting the ob served pairs (x l' YI)' (x ' Y2)' . . . , (x , Y n) into a diagram with x 2 n measured along the horizontal axis and y along the vertical axis it rarely occurs that all points lie on a straight line. Generally, no b 1 and b exist such that Yi = b + b x for i = 1,2, . . . ,n. Unless 2 l 2 i the diagram clearly suggests another type of relation, for instance quadratic or exponential, it is customary to adopt linearity in order to keep the analysis as simple as possible.

Author : Shayle R. Searle
Publisher : John Wiley & Sons
ISBN 13 : 1118952847
Total Pages : 696 pages
Book Rating : 4.49/5 ( download)

DOWNLOAD NOW!

Download or read book Linear Models written by Shayle R. Searle and published by John Wiley & Sons. This book was released on 2016-09-23 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an easy-to-understand guide to statistical linear models and its uses in data analysis This book defines a broad spectrum of statistical linear models that is useful in the analysis of data. Considerable rewriting was done to make the book more reader friendly than the first edition. Linear Models, Second Edition is written in such a way as to be self-contained for a person with a background in basic statistics, calculus and linear algebra. The text includes numerous applied illustrations, numerical examples, and exercises, now augmented with computer outputs in SAS and R. Also new to this edition is: • A greatly improved internal design and format • A short introductory chapter to ease understanding of the order in which topics are taken up • Discussion of additional topics including multiple comparisons and shrinkage estimators • Enhanced discussions of generalized inverses, the MINQUE, Bayes and Maximum Likelihood estimators for estimating variance components Furthermore, in this edition, the second author adds many pedagogical elements throughout the book. These include numbered examples, end-of-example and end-of-proof symbols, selected hints and solutions to exercises available on the book’s website, and references to “big data” in everyday life. Featuring a thorough update, Linear Models, Second Edition includes: • A new internal format, additional instructional pedagogy, selected hints and solutions to exercises, and several more real-life applications • Many examples using SAS and R with timely data sets • Over 400 examples and exercises throughout the book to reinforce understanding Linear Models, Second Edition is a textbook and a reference for upper-level undergraduate and beginning graduate-level courses on linear models, statisticians, engineers, and scientists who use multiple regression or analysis of variance in their work. SHAYLE R. SEARLE, PhD, was Professor Emeritus of Biometry at Cornell University. He was the author of the first edition of Linear Models, Linear Models for Unbalanced Data, and Generalized, Linear, and Mixed Models (with Charles E. McCulloch), all from Wiley. The first edition of Linear Models appears in the Wiley Classics Library. MARVIN H. J. GRUBER, PhD, is Professor Emeritus at Rochester Institute of Technology, School of Mathematical Sciences. Dr. Gruber has written a number of papers and has given numerous presentations at professional meetings during his tenure as a professor at RIT. His fields of interest include regression estimators and the improvement of their efficiency using shrinkage estimators. He has written and published two books on this topic. Another of his books, Matrix Algebra for Linear Models, also published by Wiley, provides good preparation for studying Linear Models. He is a member of the American Mathematical Society, the Institute of Mathematical Statistics and the American Statistical Association.

Author : Bent Jorgensen
Publisher : Routledge
ISBN 13 : 1351408615
Total Pages : 185 pages
Book Rating : 4.15/5 ( download)

DOWNLOAD NOW!

Download or read book Theory of Linear Models written by Bent Jorgensen and published by Routledge. This book was released on 2019-01-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a self-contained exposition of the theory of linear models, this treatise strikes a compromise between theory and practice, providing a sound theoretical basis while putting the theory to work in important cases.

Author : George Seber
Publisher : Springer
ISBN 13 : 3319219308
Total Pages : 208 pages
Book Rating : 4.01/5 ( download)

DOWNLOAD NOW!

Download or read book The Linear Model and Hypothesis written by George Seber and published by Springer. This book was released on 2015-10-08 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ronald Christensen
Publisher : Springer Science & Business Media
ISBN 13 : 9780387953618
Total Pages : 502 pages
Book Rating : 4.12/5 ( download)

DOWNLOAD NOW!

Download or read book Plane Answers to Complex Questions written by Ronald Christensen and published by Springer Science & Business Media. This book was released on 2002 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: ANOVA, estimation including Bayesian estimation, hypothesis testing, 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: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes discussion of identifiability and its relationship to estimability, different approaches to the theories of testing parametric hypotheses and analysis of covariance, additional discussion of the geometry of least squares estimation and testing, new discussion of models for experiments with factorial treatment structures, and a new appendix on possible causes for getting test statistics that are so small as to be suspicious. Ronald Christensen is a Professor of Statistics at the University of New Mexico. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.

Author : Cornelis Dubbelman
Publisher :
ISBN 13 : 9789020707731
Total Pages : 0 pages
Book Rating : 4.36/5 ( download)

DOWNLOAD NOW!

Download or read book Disturbances in the Linear Model, Estimation and Hypothesis Testing written by Cornelis Dubbelman and published by . This book was released on 1978 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Annette J. Dobson
Publisher : Springer
ISBN 13 : 1489931740
Total Pages : 133 pages
Book Rating : 4.40/5 ( download)

DOWNLOAD NOW!

Download or read book Introduction to Statistical Modelling written by Annette J. Dobson and published by Springer. This book was released on 2013-11-11 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about generalized linear models as described by NeIder and Wedderburn (1972). This approach provides a unified theoretical and computational framework for the most commonly used statistical methods: regression, analysis of variance and covariance, logistic regression, log-linear models for contingency tables and several more specialized techniques. More advanced expositions of the subject are given by McCullagh and NeIder (1983) and Andersen (1980). The emphasis is on the use of statistical models to investigate substantive questions rather than to produce mathematical descriptions of the data. Therefore parameter estimation and hypothesis testing are stressed. I have assumed that the reader is familiar with the most commonly used statistical concepts and methods and has some basic knowledge of calculus and matrix algebra. Short numerical examples are used to illustrate the main points. In writing this book I have been helped greatly by the comments and criticism of my students and colleagues, especially Anne Young. However, the choice of material, and the obscurities and errors are my responsibility and I apologize to the reader for any irritation caused by them. For typing the manuscript under difficult conditions I am grateful to Anne McKim, Jan Garnsey, Cath Claydon and Julie Latimer.