Hypothesis Tests with Multiple Linear Inequality Constraints PDF Download

Author: Yu-Min Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 292

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Author: Johan C. Akkerboom
Publisher: Springer Science & Business Media
ISBN: 1461233925
Category : Mathematics
Languages : en
Pages : 303

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Book Description
Represents a self-contained account of a new promising and generally applicable approach to a large class of one-sided testing problems, where the alternative is restricted by at least two linear inequalities. It highlights the geometrical structure of these problems. It gives guidance in the construction of a so-called Circular Likelihood Ratio (CLR) test, which is obtained if the linear inequalities, or polyhedral cone, are replaced by one suitable angular inequality, or circular cone. Such a test will often constitute a nice and easy-to-use compromise between the LR-test and a suitable linear test against the original alternative. The book treats both theory and practice of CLR-tests. For cases with up to 13 linear inequalities, it evaluates the power of CLR-tests, derives the most stringent CLR-test, and provides tables of critical values. It is of interest both to the specialist in order- restricted inference and to the statistical consultant in need of simple and powerful one-sided tests. Many examples are worked out for ANOVA, goodness-of-fit, and contingency table problems. Case studies are devoted to Mokken's one- dimensional scaling model, one-sided treatment comparison in a two-period crossover trial, and some real data ANOVA- layouts (biology and educational psychology).

Author: David A. Harville
Publisher: CRC Press
ISBN: 1000983811
Category : Mathematics
Languages : en
Pages : 1030

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Book Description
Linear Models and the Relevant Distributions and Matrix Algebra: A Unified Approach, Volume 2 covers several important topics that were not included in the first volume. The second volume complements the first, providing detailed solutions to the exercises in both volumes, thereby greatly enhancing its appeal for use in advanced statistics programs. This volume can serve as a valuable reference. It can also serve as a resource in a mathematical statistics course for use in illustrating various theoretical concepts in the context of a relatively complex setting of great practical importance. Together with the first volume, this volume provides a largely self-contained treatment of an important area of statistics and should prove highly useful to graduate students and others. Key Features: • Includes solutions to the exercises from both the first and second volumes • Includes coverage of several topics not covered in the first volume • Highly valuable as a reference book for graduate students and researchers

Author: Ning-zhong Shi
Publisher: World Scientific Publishing Company
ISBN: 9813107219
Category : Mathematics
Languages : en
Pages : 320

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This book presents up-to-date theory and methods of statistical hypothesis testing based on measure theory. The so-called statistical space is a measurable space adding a family of probability measures. Most topics in the book will be developed based on this term. The book includes some typical data sets, such as the relation between race and the death penalty verdict, the behavior of food intake of two kinds of Zucker rats, and the per capita income and expenditure in China during the 1978-2002 period. Emphasis is given to the process of finding appropriate statistical techniques and methods of evaluating these techniques.

Author: Otto Opitz
Publisher: Springer Science & Business Media
ISBN: 3642750400
Category : Business & Economics
Languages : en
Pages : 550

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The 13th conference of the Gesellschaft fUr Klassifikation e. V. took place at the Universitat Augsburg from April 10 to 12, 1989, with the' local organization by the Lehrstuhl fUr Mathematische Me thoden der Wirtschaftswissenschaften. The wide ranged subject of the conference Conceptual and Numerical Analysis of Data was obliged to indicate the variety of the concepts of data and information as well as the manifold methods of analysing and structuring. Based on the received announcements of papers four sections have been arranged: 1. Data Analysis and Classification: Basic Concepts and Methods 2. Applications in Library Sciences, Documentation and Information Sciences 3. Applications in Economics and Social Sciences 4. Applications in Natural Sciences and Computer Sciences This classification doesn't separate strictly, but it shows that theo retic and applying researchers of most different disciplines were disposed to present a paper. In 60 survey and special lectures the speakers reported on developments in theory and applications en couraging the interdisciplinary dialogue of all participants. This volume contains 42 selected papers grouped according to the four sections. Now we give a short insight into the presented papers. x Several problems of concept analysis, cluster analysis, data analysis and multivariate statistics are considered in 18 pa pers of section 1. The geometric representation of a concept lattice is a collection of figures in the plane corresponding to the given concepts in such a way that the subconcept-superconcept-relation corresponds to the containment relation between the figures. R.

Author: Mervyn J. Silvapulle
Publisher: John Wiley & Sons
ISBN: 1118165632
Category : Mathematics
Languages : en
Pages : 560

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An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. This volume enables professionals in these and related fields to master the concepts of statistical inference under inequality constraints and to apply the theory to problems in a variety of areas. Constrained Statistical Inference: Order, Inequality, and Shape Constraints provides a unified and up-to-date treatment of the methodology. It clearly illustrates concepts with practical examples from a variety of fields, focusing on sociology, econometrics, and biostatistics. The authors also discuss a broad range of other inequality-constrained inference problems that do not fit well in the contemplated unified framework, providing a meaningful way for readers to comprehend methodological resolutions. Chapter coverage includes: Population means and isotonic regression Inequality-constrained tests on normal means Tests in general parametric models Likelihood and alternatives Analysis of categorical data Inference on monotone density function, unimodal density function, shape constraints, and DMRL functions Bayesian perspectives, including Stein’s Paradox, shrinkage estimation, and decision theory

Author: Virendera K. Srivastava
Publisher: CRC Press
ISBN: 1000148939
Category : Mathematics
Languages : en
Pages : 398

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This book brings together the scattered literature associated with the seemingly unrelated regression equations (SURE) model used by econometricians and others. It focuses on the theoretical statistical results associated with the SURE model.

Author: Herbert Hoijtink
Publisher: CRC Press
ISBN: 1439880514
Category : Mathematics
Languages : en
Pages : 243

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Book Description
When scientists formulate their theories, expectations, and hypotheses, they often use statements like: ``I expect mean A to be bigger than means B and C"; ``I expect that the relation between Y and both X1 and X2 is positive"; and ``I expect the relation between Y and X1 to be stronger than the relation between Y and X2". Stated otherwise, they formulate their expectations in terms of inequality constraints among the parameters in which they are interested, that is, they formulate Informative Hypotheses. There is currently a sound theoretical foundation for the evaluation of informative hypotheses using Bayes factors, p-values and the generalized order restricted information criterion. Furthermore, software that is often free is available to enable researchers to evaluate the informative hypotheses using their own data. The road is open to challenge the dominance of the null hypothesis for contemporary research in behavioral, social, and other sciences.

Author: Thomas B. Fomby
Publisher: Springer Science & Business Media
ISBN: 1441987460
Category : Business & Economics
Languages : en
Pages : 637

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Book Description
This book had its conception in 1975in a friendly tavern near the School of Businessand PublicAdministration at the UniversityofMissouri-Columbia. Two of the authors (Fomby and Hill) were graduate students of the third (Johnson), and were (and are) concerned about teaching econometrics effectively at the graduate level. We decided then to write a book to serve as a comprehensive text for graduate econometrics. Generally, the material included in the bookand itsorganization have been governed by the question, " Howcould the subject be best presented in a graduate class?" For content, this has meant that we have tried to cover " all the bases " and yet have not attempted to be encyclopedic. The intended purpose has also affected the levelofmathematical rigor. We have tended to prove only those results that are basic and/or relatively straightforward. Proofs that would demand inordinant amounts of class time have simply been referenced. The book is intended for a two-semester course and paced to admit more extensive treatment of areas of specific interest to the instructor and students. We have great confidence in the ability, industry, and persistence of graduate students in ferreting out and understanding the omitted proofs and results. In the end, this is how one gains maturity and a fuller appreciation for the subject in any case. It is assumed that the readers of the book will have had an econometric methods course, using texts like J. Johnston's Econometric Methods, 2nd ed.

Author: Pierre Moulin
Publisher: Cambridge University Press
ISBN: 1107185920
Category : Mathematics
Languages : en
Pages : 423

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Book Description
A mathematically accessible textbook introducing all the tools needed to address modern inference problems in engineering and data science.