Introduction To Robust And Quasi Robust Statistical Methods

A broad and unified methodology for robust statistics—with exciting new applications Robust statistics is one of the fastest growing fields in contemporary statistics. It is also one of the more diverse and sometimes confounding areas, given the many different assessments and interpretations of robustness by theoretical and applied statisticians. This innovative book unifies the many varied, yet related, concepts of robust statistics under a sound theoretical modulation. It seamlessly integrates asymptotics and interrelations, and provides statisticians with an effective system for dealing with the interrelations between the various classes of procedures. Drawing on the expertise of researchers from around the world, and covering over a decade's worth of developments in the field, Robust Statistical Procedures: Asymptotics and Interrelations: Discusses both theory and applications in its two parts, from the fundamentals to robust statistical inference Thoroughly explores the interrelations between diverse classes of procedures, unlike any other book Compares nonparametric procedures with robust statistics, explaining in detail asymptotic representations for various estimators Provides a timesaving list of mathematical tools for the problems under discussion Keeps mathematical abstractions to a minimum, in spite of its largely theoretical content Includes useful problems and exercises at the end of each chapter Offers strategies for more complex models when using robust statistical procedures Self-contained and rounded in approach, this book is invaluable for both applied statisticians and theoretical researchers; for graduate students in mathematical statistics; and for anyone interested in the influence of this methodology.

The second edition of Robust Statistical Methods with R provides a systematic treatment of robust procedures with an emphasis on new developments and on the computational aspects. There are many numerical examples and notes on the R environment, and the updated chapter on the multivariate model contains additional material on visualization of multivariate data in R. A new chapter on robust procedures in measurement error models concentrates mainly on the rank procedures, less sensitive to errors than other procedures. This book will be an invaluable resource for researchers and postgraduate students in statistics and mathematics. Features • Provides a systematic, practical treatment of robust statistical methods • Offers a rigorous treatment of the whole range of robust methods, including the sequential versions of estimators, their moment convergence, and compares their asymptotic and finite-sample behavior • The extended account of multivariate models includes the admissibility, shrinkage effects and unbiasedness of two-sample tests • Illustrates the small sensitivity of the rank procedures in the measurement error model • Emphasizes the computational aspects, supplies many examples and illustrations, and provides the own procedures of the authors in the R software on the book’s website

Here is a brief, well-organized, and easy-to-follow introduction and overview of robust statistics. Huber focuses primarily on the important and clearly understood case of distribution robustness, where the shape of the true underlying distribution deviates slightly from the assumed model (usually the Gaussian law). An additional chapter on recent developments in robustness has been added and the reference list has been expanded and updated from the 1977 edition.

Robust statistical methods were developed to supplement the classical procedures when the data violate classical assumptions. They are ideally suited to applied research across a broad spectrum of study, yet most books on the subject are narrowly focused, overly theoretical, or simply outdated. Robust Statistical Methods with R provides a systemati

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.

Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions. New to this edition 35% revised content Covers many new and improved R functions New techniques that deal with a wide range of situations Extensive revisions to cover the latest developments in robust regression Covers latest improvements in ANOVA Includes newest rank-based methods Describes and illustrated easy to use software