Robust Diagnostic Regression Analysis

Robust Diagnostic Regression Analysis PDF

Author: Anthony Atkinson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 342

ISBN-13: 1461211603

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Graphs are used to understand the relationship between a regression model and the data to which it is fitted. The authors develop new, highly informative graphs for the analysis of regression data and for the detection of model inadequacies. As well as illustrating new procedures, the authors develop the theory of the models used, particularly for generalized linear models. The book provides statisticians and scientists with a new set of tools for data analysis. Software to produce the plots is available on the authors website.

Regression Diagnostics

Regression Diagnostics PDF

Author: John Fox

Publisher: SAGE Publications

Published: 2019-12-09

Total Pages: 138

ISBN-13: 1544375212

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Regression diagnostics are methods for determining whether a regression model that has been fit to data adequately represents the structure of the data. For example, if the model assumes a linear (straight-line) relationship between the response and an explanatory variable, is the assumption of linearity warranted? Regression diagnostics not only reveal deficiencies in a regression model that has been fit to data but in many instances may suggest how the model can be improved. The Second Edition of this bestselling volume by John Fox considers two important classes of regression models: the normal linear regression model (LM), in which the response variable is quantitative and assumed to have a normal distribution conditional on the values of the explanatory variables; and generalized linear models (GLMs) in which the conditional distribution of the response variable is a member of an exponential family. R code and data sets for examples within the text can be found on an accompanying website.

Directions in Robust Statistics and Diagnostics

Directions in Robust Statistics and Diagnostics PDF

Author: Werner Stahel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 384

ISBN-13: 1461244447

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This IMA Volume in Mathematics and its Applications DIRECTIONS IN ROBUST STATISTICS AND DIAGNOSTICS is based on the proceedings of the first four weeks of the six week IMA 1989 summer program "Robustness, Diagnostics, Computing and Graphics in Statistics". An important objective of the organizers was to draw a broad set of statisticians working in robustness or diagnostics into collaboration on the challenging problems in these areas, particularly on the interface between them. We thank the organizers of the robustness and diagnostics program Noel Cressie, Thomas P. Hettmansperger, Peter J. Huber, R. Douglas Martin, and especially Werner Stahel and Sanford Weisberg who edited the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Central themes of all statistics are estimation, prediction, and making decisions under uncertainty. A standard approach to these goals is through parametric mod elling. Parametric models can give a problem sufficient structure to allow standard, well understood paradigms to be applied to make the required inferences. If, how ever, the parametric model is not completely correct, then the standard inferential methods may not give reasonable answers. In the last quarter century, particularly with the advent of readily available computing, more attention has been paid to the problem of inference when the parametric model used is not correctly specified.

Robust Regression and Outlier Detection

Robust Regression and Outlier Detection PDF

Author: Peter J. Rousseeuw

Publisher: John Wiley & Sons

Published: 2005-02-25

Total Pages: 329

ISBN-13: 0471725374

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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

Modern Methods for Robust Regression

Modern Methods for Robust Regression PDF

Author: Robert Andersen

Publisher: SAGE

Published: 2008

Total Pages: 129

ISBN-13: 1412940729

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Offering an in-depth treatment of robust and resistant regression, this volume takes an applied approach and offers readers empirical examples to illustrate key concepts.

Robust Methods in Regression Analysis – Theory and Application

Robust Methods in Regression Analysis – Theory and Application PDF

Author: Robert Finger

Publisher: GRIN Verlag

Published: 2007-05-06

Total Pages: 120

ISBN-13: 3638634507

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Diploma Thesis from the year 2006 in the subject Mathematics - Statistics, grade: 1.3, European University Viadrina Frankfurt (Oder) (Wirtschaftswissenschaftliche Fakultät), language: English, abstract: Regression Analysis is an important statistical tool for many applications. The most frequently used approach to Regression Analysis is the method of Ordinary Least Squares. But this method is vulnerable to outliers; even a single outlier can spoil the estimation completely. How can this vulnerability be described by theoretical concepts and are there alternatives? This thesis gives an overview over concepts and alternative approaches. The three fundamental approaches to Robustness (qualitative-, infinitesimal- and quantitative Robustness) are introduced in this thesis and are applied to different estimators. The estimators under study are measures of location, scale and regression. The Robustness approaches are important for the theoretical judgement of certain estimators but as well for the development of alternatives to classical estimators. This thesis focuses on the (Robustness-) performance of estimators if outliers occur within the data set. Measures of location and scale provide necessary steppingstones into the topic of Regression Analysis. In particular the median and trimming approaches are found to produce very robust results. These results are used in Regression Analysis to find alternatives to the method of Ordinary Least Squares. Its vulnerability can be overcome by applying the methods of Least Median of Squares or Least Trimmed Squares. Different outlier diagnostic tools are introduced to improve the poor efficiency of these Regression Techniques. Furthermore, this thesis delivers a simulation of some Regression Techniques on different situations in Regression Analysis. This simulation focuses in particular on changes in regression estimates if outliers occur in the data. Theoretically derived results as well as the results of the simulation lead to the recommendation of the method of Reweighted Least Squares. Applying this method frequently on problems of Regression Analysis provides outlier resistant and efficient estimates.

Robust Methods in Biostatistics

Robust Methods in Biostatistics PDF

Author: Stephane Heritier

Publisher: John Wiley & Sons

Published: 2009-05-11

Total Pages: 292

ISBN-13: 9780470740545

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Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers. Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust estimation, testing, model selection, model check and diagnostics. They are developed for the following general classes of models: Linear regression Generalized linear models Linear mixed models Marginal longitudinal data models Cox survival analysis model The methods are introduced both at a theoretical and applied level within the framework of each general class of models, with a particular emphasis put on practical data analysis. This book is of particular use for research students,applied statisticians and practitioners in the health field interested in more stable statistical techniques. An accompanying website provides R code for computing all of the methods described, as well as for analyzing all the datasets used in the book.

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