Robust Estimates Of Location
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| Author | : David F. Andrews |
| Publisher | : Princeton University Press |
| Total Pages | : 384 |
| Release | : 2015-03-08 |
| Genre | : Mathematics |
| ISBN | : 1400867010 |
Because estimation involves inferring information about an unknown quantity on the basis of available data, the selection of an estimator is influenced by its ability to perform well under the conditions that are assumed to underlie the data. Since these conditions are never known exactly, the estimators chosen must be robust; i.e., they must be able to perform well under a variety of underlying conditions. The theory of robust estimation is based on specified properties of specified estimators under specified conditions. This book was written as the result of a study undertaken to establish the interaction of these three components over as large a range as possible. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
| Author | : Samuel Kotz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 576 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461206677 |
Volume III includes more selections of articles that have initiated fundamental changes in statistical methodology. It contains articles published before 1980 that were overlooked in the previous two volumes plus articles from the 1980's - all of them chosen after consulting many of today's leading statisticians.
| Author | : Ricardo A. Maronna |
| Publisher | : John Wiley & Sons |
| Total Pages | : 466 |
| Release | : 2019-01-04 |
| Genre | : Mathematics |
| ISBN | : 1119214688 |
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.
| Author | : Frank R. Hampel |
| Publisher | : John Wiley & Sons |
| Total Pages | : 502 |
| Release | : 2011-09-20 |
| Genre | : Mathematics |
| ISBN | : 1118150686 |
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.
| Author | : Rand R. Wilcox |
| Publisher | : Academic Press |
| Total Pages | : 713 |
| Release | : 2012-01-12 |
| Genre | : Mathematics |
| ISBN | : 0123869838 |
"This book focuses on the practical aspects of modern and robust statistical methods. The increased accuracy and power of modern methods, versus conventional approaches to the analysis of variance (ANOVA) and regression, is remarkable. Through a combination of theoretical developments, improved and more flexible statistical methods, and the power of the computer, it is now possible to address problems with standard methods that seemed insurmountable only a few years ago"--
| Author | : Robert L. Launer |
| Publisher | : |
| Total Pages | : 330 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : |
An introduction to robust estimation; The robustness of residual displays; Robust smoothing; Robust pitman-like estimators; Robust estimation in the presence of outliers; Study of robustness by simulation: particularly improvement by adjustment and combination; Robust techniques for the user; Application of robust regression to trajectory data reduction; Tests for censoring of extreme values (especially) when population distributions are incompletely defined; Robust estimation for time series autoregressions; Robust techniques in communication; Robustness in the strategy of scientific model building; A density-quantile function perspective on robust.
| Author | : Georgy L. Shevlyakov |
| Publisher | : John Wiley & Sons |
| Total Pages | : 353 |
| Release | : 2016-09-19 |
| Genre | : Mathematics |
| ISBN | : 1118493451 |
This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data. Key features: Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields. Focuses on implementation of methodology and application of robust correlation with R. Introduces the main approaches in robust statistics, such as Huber’s minimax approach and Hampel’s approach based on influence functions. Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates. Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data. Includes an accompanying website featuring computer code and datasets Features exercises and examples throughout the text using both small and large data sets. Theoretical and applied statisticians, specialists in multivariate statistics, robust statistics, robust time series analysis, data analysis and signal processing will benefit from this book. Practitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful.
| Author | : Robert Andersen |
| Publisher | : SAGE |
| Total Pages | : 129 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 1412940729 |
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.
| Author | : Anatoli Juditsky |
| Publisher | : Princeton University Press |
| Total Pages | : 655 |
| Release | : 2020-04-07 |
| Genre | : Mathematics |
| ISBN | : 0691197296 |
This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences. Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems—sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals—demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems. Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.
| Author | : Robert L. Launer |
| Publisher | : Academic Press |
| Total Pages | : 313 |
| Release | : 2014-05-12 |
| Genre | : Mathematics |
| ISBN | : 1483263363 |
Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.
