Parameter Estimation And Hypothesis Testing In Linear Models
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Parameter Estimation And Hypothesis Testing In Linear Models
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Author : Karl-Rudolf Koch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Parameter Estimation And Hypothesis Testing In Linear Models written by Karl-Rudolf Koch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Advanced Linear Models
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Author : Shein-Chung Chow
language : en
Publisher: Routledge
Release Date : 2018-05-04
Advanced Linear Models written by Shein-Chung Chow and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
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.
Disturbances In The Linear Model Estimation And Hypothesis Testing
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Author : C. Dubbelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Disturbances In The Linear Model Estimation And Hypothesis Testing written by C. Dubbelman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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.
The Linear Hypothesis
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Author : George Arthur Frederick Seber
language : en
Publisher:
Release Date : 1980
The Linear Hypothesis written by George Arthur Frederick Seber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematical statistics categories.
The Linear Model And Hypothesis
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Author : George Seber
language : en
Publisher: Springer
Release Date : 2015-10-08
The Linear Model And Hypothesis written by George Seber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.
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.
Linear Models
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Author : Shayle R. Searle
language : en
Publisher: John Wiley & Sons
Release Date : 2016-09-23
Linear Models written by Shayle R. Searle and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-23 with Mathematics categories.
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.
Disturbances In The Linear Model Estimation And Hypothesis Testing
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Author : Cornelis Dubbelman
language : en
Publisher:
Release Date : 1978
Disturbances In The Linear Model Estimation And Hypothesis Testing written by Cornelis Dubbelman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Econometrics categories.
Statistics With Jmp Hypothesis Tests Anova And Regression
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Author : Peter Goos
language : en
Publisher: John Wiley & Sons
Release Date : 2016-02-16
Statistics With Jmp Hypothesis Tests Anova And Regression written by Peter Goos and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-16 with Mathematics categories.
Statistics with JMP: Hypothesis Tests, ANOVA and Regression Peter Goos, University of Leuven and University of Antwerp, Belgium David Meintrup, University of Applied Sciences Ingolstadt, Germany A first course on basic statistical methodology using JMP This book provides a first course on parameter estimation (point estimates and confidence interval estimates), hypothesis testing, ANOVA and simple linear regression. The authors approach combines mathematical depth with numerous examples and demonstrations using the JMP software. Key features: Provides a comprehensive and rigorous presentation of introductory statistics that has been extensively classroom tested. Pays attention to the usual parametric hypothesis tests as well as to non-parametric tests (including the calculation of exact p-values). Discusses the power of various statistical tests, along with examples in JMP to enable in-sight into this difficult topic. Promotes the use of graphs and confidence intervals in addition to p-values. Course materials and tutorials for teaching are available on the book's companion website. Masters and advanced students in applied statistics, industrial engineering, business engineering, civil engineering and bio-science engineering will find this book beneficial. It also provides a useful resource for teachers of statistics particularly in the area of engineering.
Simultaneous Inference In Regression
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Author : Wei Liu
language : en
Publisher: CRC Press
Release Date : 2010-10-19
Simultaneous Inference In Regression written by Wei Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-19 with Mathematics categories.
Simultaneous confidence bands enable more intuitive and detailed inference of regression analysis than the standard inferential methods of parameter estimation and hypothesis testing. Simultaneous Inference in Regression provides a thorough overview of the construction methods and applications of simultaneous confidence bands for various inferentia
Introduction To Statistical Modelling
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Author : Annette J. Dobson
language : en
Publisher: Springer
Release Date : 2013-11-11
Introduction To Statistical Modelling written by Annette J. Dobson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.