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Hilbert Space Methods in Probability and Statistical Inference

Hilbert Space Methods in Probability and Statistical Inference
Author: Christopher G. Small
Publisher: John Wiley & Sons
Total Pages: 268
Release: 2011-09-15
Genre: Mathematics
ISBN: 1118165535

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Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.


Aspects of Statistical Inference

Aspects of Statistical Inference
Author: A. H. Welsh
Publisher: John Wiley & Sons
Total Pages: 480
Release: 2011-09-15
Genre: Mathematics
ISBN: 1118165438

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Relevant, concrete, and thorough--the essential data-based text onstatistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertly synthesizesbroad, critical theory with concrete data and relevant topics. Thetext follows a historical framework, uses real-data sets andstatistical graphics, and treats multiparameter problems, yet isultimately about the concepts themselves. Written with clarity and depth, Aspects of Statistical Inference: * Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches * Illustrates methods with real-data sets on diabetic retinopathy,the pharmacological effects of caffeine, stellar velocity, andindustrial experiments * Considers multiparameter problems * Develops large sample approximations and shows how to use them * Presents the philosophy and application of robustness theory * Highlights the central role of randomization in statistics * Uses simple proofs to illuminate foundational concepts * Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing and presentingthe latest approaches to statistical inference.


Comparative Statistical Inference

Comparative Statistical Inference
Author: Vic Barnett
Publisher: John Wiley & Sons
Total Pages: 418
Release: 1999-08-03
Genre: Mathematics
ISBN: 9780471976431

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This fully updated and revised third edition, presents a wide ranging, balanced account of the fundamental issues across the full spectrum of inference and decision-making. Much has happened in this field since the second edition was published: for example, Bayesian inferential procedures have not only gained acceptance but are often the preferred methodology. This book will be welcomed by both the student and practising statistician wishing to study at a fairly elementary level, the basic conceptual and interpretative distinctions between the different approaches, how they interrelate, what assumptions they are based on, and the practical implications of such distinctions. As in earlier editions, the material is set in a historical context to more powerfully illustrate the ideas and concepts. Includes fully updated and revised material from the successful second edition Recent changes in emphasis, principle and methodology are carefully explained and evaluated Discusses all recent major developments Particular attention is given to the nature and importance of basic concepts (probability, utility, likelihood etc) Includes extensive references and bibliography Written by a well-known and respected author, the essence of this successful book remains unchanged providing the reader with a thorough explanation of the many approaches to inference and decision making.


Bayesian Analysis in Statistics and Econometrics

Bayesian Analysis in Statistics and Econometrics
Author: Donald A. Berry
Publisher: John Wiley & Sons
Total Pages: 610
Release: 1996
Genre: Business & Economics
ISBN: 9780471118565

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This book is a definitive work that captures the current state of knowledge of Bayesian Analysis in Statistics and Econometrics and attempts to move it forward. It covers such topics as foundations, forecasting inferential matters, regression, computation and applications.


Constrained Statistical Inference

Constrained Statistical Inference
Author: Mervyn J. Silvapulle
Publisher: John Wiley & Sons
Total Pages: 560
Release: 2011-09-15
Genre: Mathematics
ISBN: 1118165632

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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


An Introduction to Probability and Statistics

An Introduction to Probability and Statistics
Author: Vijay K. Rohatgi
Publisher: John Wiley & Sons
Total Pages: 747
Release: 2011-09-15
Genre: Mathematics
ISBN: 1118165683

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The second edition of a well-received book that was published 24 years ago and continues to sell to this day, An Introduction to Probability and Statistics is now revised to incorporate new information as well as substantial updates of existing material.


Biostatistical Methods

Biostatistical Methods
Author: John M. Lachin
Publisher: John Wiley & Sons
Total Pages: 568
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470317892

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Comprehensive coverage of classical and modern methods of biostatistics Biostatistical Methods focuses on the assessment of risks and relative risks on the basis of clinical investigations. It develops basic concepts and derives biostatistical methods through both the application of classical mathematical statistical tools and more modern likelihood-based theories. The first half of the book presents methods for the analysis of single and multiple 2x2 tables for cross-sectional, prospective, and retrospective (case-control) sampling, with and without matching using fixed and two-stage random effects models. The text then moves on to present a more modern likelihood- or model-based approach, which includes unconditional and conditional logistic regression; the analysis of count data and the Poisson regression model; and the analysis of event time data, including the proportional hazards and multiplicative intensity models. The book contains a technical appendix that presents the core mathematical statistical theory used for the development of classical and modern statistical methods. Biostatistical Methods: The Assessment of Relative Risks: * Presents modern biostatistical methods that are generalizations of the classical methods discussed * Emphasizes derivations, not just cookbook methods * Provides copious reference citations for further reading * Includes extensive problem sets * Employs case studies to illustrate application of methods * Illustrates all methods using the Statistical Analysis System(r) (SAS) Supplemented with numerous graphs, charts, and tables as well as a Web site for larger data sets and exercises, Biostatistical Methods: The Assessment of Relative Risks is an excellent guide for graduate-level students in biostatistics and an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.


A Guide to Chi-Squared Testing

A Guide to Chi-Squared Testing
Author: Priscilla E. Greenwood
Publisher: John Wiley & Sons
Total Pages: 318
Release: 1996-04-05
Genre: Mathematics
ISBN: 9780471557791

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The first step-by-step guide to conducting successful Chi-squaredtests Chi-squared testing is one of the most commonly applied statisticaltechniques. It provides reliable answers for researchers in a widerange of fields, including engineering, manufacturing, finance,agriculture, and medicine. A Guide to Chi-Squared Testing brings readers up to date on recentinnovations and important material previously published only in theformer Soviet Union. Its clear, concise treatment and practicaladvice make this an ideal reference for all researchers andconsultants. Authors Priscilla E. Greenwood and Mikhail S. Nikulin demonstratethe application of these general purpose tests in a wide variety ofspecific settings. They also * Detail the various decisions to be made when applying Chi-squaredtests to real data, and the proper application of these tests instandard hypothesis-testing situations * Describe how Chi-squared type tests allow statisticians toconstruct a test statistic whose distribution is asymptoticallyChi-squared, and to compute power against various alternatives * Devote half of the book to examples of Chi-squared tests that canbe easily adapted to situations not covered in the book * Provide a self-contained, accessible treatment of themathematical requisites * Include an extensive bibliography and suggestions for furtherreading


Robust Statistics

Robust Statistics
Author: Frank R. Hampel
Publisher: John Wiley & Sons
Total Pages: 502
Release: 2011-09-20
Genre: Mathematics
ISBN: 1118150686

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The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This is a nice book containing a wealth of information, much ofit due to the authors. . . . If an instructor designing such acourse wanted a textbook, this book would be the best choiceavailable. . . . There are many stimulating exercises, and the bookalso contains an excellent index and an extensive list ofreferences." —Technometrics "[This] book should be read carefully by anyone who isinterested in dealing with statistical models in a realisticfashion." —American Scientist Introducing concepts, theory, and applications, RobustStatistics is accessible to a broad audience, avoidingallusions to high-powered mathematics while emphasizing ideas,heuristics, and background. The text covers the approach based onthe influence function (the effect of an outlier on an estimater,for example) and related notions such as the breakdown point. Italso treats the change-of-variance function, fundamental conceptsand results in the framework of estimation of a single parameter,and applications to estimation of covariance matrices andregression parameters.


Limit Distributions for Sums of Independent Random Vectors

Limit Distributions for Sums of Independent Random Vectors
Author: Mark M. Meerschaert
Publisher: John Wiley & Sons
Total Pages: 514
Release: 2001-07-11
Genre: Mathematics
ISBN: 9780471356295

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Die Quintessenz aus über 100 Originalarbeiten! Ausgehend von den Grundpfeilern der modernen Wahrscheinlichkeitstheorie entwickeln die Autoren dieses in sich geschlossenen, gut verständlich formulierten Bandes die Theorie der unendlich teilbaren Verteilungen und der regulären Variation. Im Anschluss erarbeiten sie die allgemeine Grenzwerttheorie für unabhängige Zufallsvektoren. Dabei achten sie sorgfältig darauf, alle Aspekte in den Kontext der Wahrscheinlichkeitslehre und Statistik zu stellen und bieten dafür eine Fülle von Zusatzinformationen an.