Robust Regression and Outlier Detection

Author: Peter J. Rousseeuw
Publisher: John Wiley & Sons
ISBN: 9780471725374
Release Date: 2005-02-25
Genre: Mathematics

WILEY-INTERSCIENCE PAPERBACK SERIES 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. "The writing style is clear and informal, and much of thediscussion is oriented to application. In short, the book is akeeper." –Mathematical Geology "I would highly recommend the addition of this book to thelibraries of both students and professionals. It is a usefultextbook for the graduate student, because it emphasizes both thephilosophy and practice of robustness in regression settings, andit provides excellent examples of precise, logical proofs oftheorems. . . .Even for those who are familiar with robustness, thebook will be a good reference because it consolidates the researchin high-breakdown affine equivariant estimators and includes anextensive bibliography in robust regression, outlier diagnostics,and related methods. The aim of this book, the authors tell us, is‘to make robust regression available for everyday statisticalpractice.’ Rousseeuw and Leroy have included all of thenecessary ingredients to make this happen." –Journal of the American Statistical Association

Handbook of Regression Methods

Author: Derek Scott Young
Publisher: CRC Press
ISBN: 9781351650748
Release Date: 2017-06-15
Genre: Mathematics

This book is intended to read like a handbook for regression methods. It provides a broad survey of both standard and non-standard regression models and topics. Thus, the treatment includes topics that would typically be covered in a master's-level statistics course in regression (e.g., simple/multiple linear regression, residual analysis, and ANOVA; as well as more specialized topics like biased regression procedures, multivariate regression, and count regression models).

Datenanalyse mit Modellen f r Cluster linearer Regression

Author: Christian Hennig
ISBN: 9783832421571
Release Date: 2000-02-18
Genre: Mathematics

Inhaltsangabe:Einleitung: In dieser Arbeit geht es um die Analyse von Daten, in denen Cluster linearer Regression erwartet werden können. Ein "Cluster linearer Regression" ist ein Teildatensatz, der sich von den übrigen Daten unterscheidet in Hinsicht auf den Zusammenhang zwischen einer oder mehreren Einflußgrößen und einer abhängigen Variablen. Dieser Zusammenhang wird pro Gruppe als linear vorausgesetzt ("lineare Regression"). Es werden mehrere Verfahren analysiert, um solche Gruppen zu finden. Mit der "Fixpunktcluster-Analyse" wird ein neues Verfahren vorgestellt und mit Hilfe von statistischer Theorie und Simulations-Studien untersucht. Es hat gegenüber den "klassischen" Verfahren den Vorteil, dass Fixpunktcluster unempfindlich gegenüber Veränderungen in "entfernten" Teilen der Daten (z.B. Ausreißer) sind. Das Verfahren lässt sich auch auf andere Probleme der Clusteranalyse übertragen. Inhaltsverzeichnis:Inhaltsverzeichnis: Inhaltsverzeichnis4 English abstract 3 1.Einführung7 1.1Das Problem 7 1.2Modelle für die Clusteranalyse (Teil I) 9 1.3Exkurs: Angemessenheit von Modellen 10 1.4Fixpunktcluster (Teil II und III) 12 1.5Vergleich der Verfahren (Teil IV) 13 1.6Formale und stilistische Bemerkungen 14 1.7Bezeichnungen 15 I.Mischungen linearer Regressionen17 2.Modellierung17 3.Ansätze zur Analyse der Modelle22 3.1Wechselpunktprobleme 22 3.2Kleinste Quadrate 23 3.3Parameterschätzung im Mischmodell 24 3.4Parameterschätzung im Fixed Partition Model 28 3.5Alternative Ansätze 30 3.5.1Robuste Regression 30 3.5.2Schwache Hierarchien 33 4.Einführung: Identifizierbarkeit 34 5.Beispiele für Nicht-Identfizierbarkeit 38 6.Identifizierbarkeitsresultate 43 II.Fixpunktcluster 54 7.Einführung: Fixpunktcluster 54 7.1Cluster und Ausreißer: Die allgemeine Fixpunktcluster-Idee 54 7.2Beispiel: Fixpunktcluster für 0-1-Vektoren 60 7.3Fixpunktcluster und die Selbstorganisation der Wahrnehmung 62 8.Fixpunktcluster im Regressionsfall63 8.1Regressions-Fixpunktclusterindikatoren 63 8.2Regressions-Fixpunktclustervektoren 65 9.Berechnung von KQ-Fixpunktclustervektoren67 10.Analyse von Beispieldatensätzen73 10.1Telefondaten 74 10.2Artifizieller Datensatz 76 III.Fixpunktclusterindikatoren in speziellen Modellen81 11.Hilfsresultate81 11.1Eigenschaften der Fixpunktcluster-Parameterfunktion 81 11.2Abgeschnittene Normalverteilungen 84 12.Fixpunktclusterindikatoren in homogenen Modellen91 13.Fixpunktclusterindikatoren in [...]

Robust Nonlinear Regression

Author: Hossein Riazoshams
Publisher: John Wiley & Sons
ISBN: 9781119010449
Release Date: 2018-06-11
Genre: Mathematics

The first book to discuss robust aspects of nonlinear regression—with applications using R software Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers. The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets. The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression Addresses some commonly mishandled aspects of modeling R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying website Robust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.

Applied Linear Regression

Author: Sanford Weisberg
Publisher: Wiley
ISBN: UOM:39015059097769
Release Date: 1985-08-14
Genre: Mathematics

Nonlinear Statistical Methods A. Ronald Gallant Describes the recent advances in statistical and probability theory that have removed obstacles to an adequate theory of estimation and inference for nonlinear models. Thoroughly explains theory, methods, computations, and applications. Covers the three major categories of statistical models that relate dependent variables to explanatory variables: univariate regression models, multivariate regression models, and simultaneous equations models. Includes many figures which illustrate computations with SAS(R) code and resulting output. 1987 (0 471-80260-3) 610 pp. Exploring Data Tables, Trends, and Shapes Edited by David C. Hoaglin, Frederick Mosteller, and John W. Tukey Together with its companion volume, Understanding Robust and Exploratory Data Analysis, this work provides a definitive account of exploratory and robust/resistant statistics. It presents a variety of more advanced techniques and extensions of basic exploratory tools, explains why these further developments are valuable, and provides insight into how and why they were invented. In addition to illustrating these techniques, the book traces aspects of their development from classical statistical theory. 1985 (0 471-09776-4) 672 pp. Robust Regression & Outlier Detection Peter J. Rousseeuw and Annick M. Leroy An introduction to robust statistical techniques that have been developed to isolate or identify outliers. Emphasizes simple, intuitive ideas and their application in actual use. No prior knowledge of the field is required. Discusses robustness in regression, simple regression, robust multiple regression, the special case of one-dimensional location, and outlier diagnostics. Also presents an outlook of robustness in related fields such as time series analysis. Emphasizes "high-breakdown" methods that can cope with a sizable fraction of contamination. Focuses on the least median of squares method, which appeals to the intuition and is easy to use. 1987 (0 471-85233-3) 329 pp.

Robust Statistics

Author: Frank R. Hampel
Publisher: John Wiley & Sons
ISBN: 9781118150689
Release Date: 2011-09-20
Genre: Mathematics

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.

Weibull Models

Author: D. N. Prabhakar Murthy
Publisher: John Wiley & Sons
ISBN: 0471473278
Release Date: 2004-01-28
Genre: Mathematics

A comprehensive perspective on Weibull models The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume. This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research. Organized into seven distinct parts, Weibull Models: Covers model analysis, parameter estimation, model validation,and application Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner Intertwines theory and application Focuses on model identification prior to model parameterestimation Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set Highlights the use of Weibull models in reliability theory Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.

Robust Statistics

Author: Peter J. Huber
Publisher: John Wiley & Sons
ISBN: 0471650722
Release Date: 2004
Genre: Mathematics

The first systematic, book-length treatment of the subject. Begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. Stresses concepts. Provides selected numerical algorithms for computing robust estimates, as well as convergence proofs. Tables contain quantitative robustness information for a variety of estimates.

Longitudinal Data Analysis

Author: Donald Hedeker
Publisher: John Wiley & Sons
ISBN: 9780470036471
Release Date: 2006-05-12
Genre: Mathematics

Longitudinal data analysis for biomedical and behavioral sciences This innovative book sets forth and describes methods for the analysis of longitudinaldata, emphasizing applications to problems in the biomedical and behavioral sciences. Reflecting the growing importance and use of longitudinal data across many areas of research, the text is designed to help users of statistics better analyze and understand this type of data. Much of the material from the book grew out of a course taught by Dr. Hedeker on longitudinal data analysis. The material is, therefore, thoroughly classroom tested and includes a number of features designed to help readers better understand and apply the material. Statistical procedures featured within the text include: * Repeated measures analysis of variance * Multivariate analysis of variance for repeated measures * Random-effects regression models (RRM) * Covariance-pattern models * Generalized-estimating equations (GEE) models * Generalizations of RRM and GEE for categorical outcomes Practical in their approach, the authors emphasize the applications of the methods, using real-world examples for illustration. Some syntax examples are provided, although the authors do not generally focus on software in this book. Several datasets and computer syntax examples are posted on this title's companion Web site. The authors intend to keep the syntax examples current as new versions of the software programs emerge. This text is designed for both undergraduate and graduate courses in longitudinal data analysis. Instructors can take advantage of overheads and additional course materials available online for adopters. Applied statisticians in biomedicine and the social sciences can also use the book as a convenient reference.

Time Series

Author: Ngai Hang Chan
Publisher: John Wiley & Sons
ISBN: 9780471461647
Release Date: 2004-04-05
Genre: Mathematics

Elements of Financial Time Series fills a gap in the market in thearea of financial time series analysis by giving both conceptualand practical illustrations. Examples and discussions in the laterchapters of the book make recent developments in time series moreaccessible. Examples from finance are maximized as much as possiblethroughout the book. * Full set of exercises is displayed at the end of eachchapter. * First seven chapters cover standard topics in time series at ahigh-intensity level. * Recent and timely developments in nonstandard time seriestechniques are illustrated with real finance examples indetail. * Examples are systemically illustrated with S-plus with codes anddata available on an associated Web site.

Regression Analysis by Example

Author: Samprit Chatterjee
Publisher: John Wiley & Sons
ISBN: 9780470055458
Release Date: 2006-10-20
Genre: Mathematics

The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Random Graphs for Statistical Pattern Recognition

Author: David J. Marchette
Publisher: John Wiley & Sons
ISBN: 0471722081
Release Date: 2005-02-11
Genre: Mathematics

A timely convergence of two widely used disciplines Random Graphs for Statistical Pattern Recognition is the firstbook to address the topic of random graphs as it applies tostatistical pattern recognition. Both topics are of vital interestto researchers in various mathematical and statistical fields andhave never before been treated together in one book. The use ofdata random graphs in pattern recognition in clustering andclassification is discussed, and the applications for bothdisciplines are enhanced with new tools for the statistical patternrecognition community. New and interesting applications for randomgraph users are also introduced. This important addition to statistical literaturefeatures: Information that previously has been available only throughscattered journal articles Practical tools and techniques for a wide range of real-worldapplications New perspectives on the relationship between patternrecognition and computational geometry Numerous experimental problems to encourage practicalapplications With its comprehensive coverage of two timely fields, enhancedwith many references and real-world examples, Random Graphs forStatistical Pattern Recognition is a valuable resource forindustry professionals and students alike.

Operational Risk

Author: Harry H. Panjer
Publisher: John Wiley & Sons
ISBN: 9780470051306
Release Date: 2006-10-13
Genre: Business & Economics

Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.

Robust Statistics

Author: Ricardo A. Maronna
Publisher: Wiley
ISBN: 9781119214687
Release Date: 2018-12-03
Genre: Mathematics

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

An Introduction to Statistical Concepts

Author: Debbie L Hahs-Vaughn
Publisher: Routledge
ISBN: 9781136490125
Release Date: 2013-06-19
Genre: Psychology

This comprehensive, flexible text is used in both one- and two-semester courses to review introductory through intermediate statistics. Instructors select the topics that are most appropriate for their course. Its conceptual approach helps students more easily understand the concepts and interpret SPSS and research results. Key concepts are simply stated and occasionally reintroduced and related to one another for reinforcement. Numerous examples demonstrate their relevance. This edition features more explanation to increase understanding of the concepts. Only crucial equations are included. In addition to updating throughout, the new edition features: New co-author, Debbie L. Hahs-Vaughn, the 2007 recipient of the University of Central Florida's College of Education Excellence in Graduate Teaching Award. A new chapter on logistic regression models for today's more complex methodologies. More on computing confidence intervals and conducting power analyses using G*Power. Many more SPSS screenshots to assist with understanding how to navigate SPSS and annotated SPSS output to assist in the interpretation of results. Extended sections on how to write-up statistical results in APA format. New learning tools including chapter-opening vignettes, outlines, and a list of key concepts, many more examples, tables, and figures, boxes, and chapter summaries. More tables of assumptions and the effects of their violation including how to test them in SPSS. 33% new conceptual, computational, and all new interpretative problems. A website that features PowerPoint slides, answers to the even-numbered problems, and test items for instructors, and for students the chapter outlines, key concepts, and datasets that can be used in SPSS and other packages, and more. Each chapter begins with an outline, a list of key concepts, and a vignette related to those concepts. Realistic examples from education and the behavioral sciences illustrate those concepts. Each example examines the procedures and assumptions and provides instructions for how to run SPSS, including annotated output, and tips to develop an APA style write-up. Useful tables of assumptions and the effects of their violation are included, along with how to test assumptions in SPSS. 'Stop and Think' boxes provide helpful tips for better understanding the concepts. Each chapter includes computational, conceptual, and interpretive problems. The data sets used in the examples and problems are provided on the web. Answers to the odd-numbered problems are given in the book. The first five chapters review descriptive statistics including ways of representing data graphically, statistical measures, the normal distribution, and probability and sampling. The remainder of the text covers inferential statistics involving means, proportions, variances, and correlations, basic and advanced analysis of variance and regression models. Topics not dealt with in other texts such as robust methods, multiple comparison and nonparametric procedures, and advanced ANOVA and multiple and logistic regression models are also reviewed. Intended for one- or two-semester courses in statistics taught in education and/or the behavioral sciences at the graduate and/or advanced undergraduate level, knowledge of statistics is not a prerequisite. A rudimentary knowledge of algebra is required.