Functional And Shape Data Analysis

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Functional and Shape Data Analysis

Author : Anuj Srivastava
Publisher : Springer
ISBN 13 : 1493940201
Total Pages : 447 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Functional and Shape Data Analysis by : Anuj Srivastava

Download or read book Functional and Shape Data Analysis written by Anuj Srivastava and published by Springer. This book was released on 2016-10-03 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Functional Data Analysis

Author : James Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 147577107X
Total Pages : 317 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Functional Data Analysis by : James Ramsay

Download or read book Functional Data Analysis written by James Ramsay and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Included here are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, applied data analysts, and to experienced researchers; and as such is of value both within statistics and across a broad spectrum of other fields. Much of the material appears here for the first time.

Functional Data Analysis with R and MATLAB

Author : James Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 0387981853
Total Pages : 213 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Functional Data Analysis with R and MATLAB by : James Ramsay

Download or read book Functional Data Analysis with R and MATLAB written by James Ramsay and published by Springer Science & Business Media. This book was released on 2009-06-29 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems

Introduction to Functional Data Analysis

Author : Piotr Kokoszka
Publisher : CRC Press
ISBN 13 : 1498746691
Total Pages : 311 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Introduction to Functional Data Analysis by : Piotr Kokoszka

Download or read book Introduction to Functional Data Analysis written by Piotr Kokoszka and published by CRC Press. This book was released on 2017-09-27 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

Analysis of Variance for Functional Data

Author : Jin-Ting Zhang
Publisher : CRC Press
ISBN 13 : 1439862745
Total Pages : 412 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Analysis of Variance for Functional Data by : Jin-Ting Zhang

Download or read book Analysis of Variance for Functional Data written by Jin-Ting Zhang and published by CRC Press. This book was released on 2013-06-18 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional linear models with functional responses, ill-conditioned functional linear models, diagnostics of functional observations, heteroscedastic ANOVA for functional data, and testing equality of covariance functions. Although the methodologies presented are designed for curve data, they can be extended to surface data. Useful for statistical researchers and practitioners analyzing functional data, this self-contained book gives both a theoretical and applied treatment of functional data analysis supported by easy-to-use MATLAB® code. The author provides a number of simple methods for functional hypothesis testing. He discusses pointwise, L2-norm-based, F-type, and bootstrap tests. Assuming only basic knowledge of statistics, calculus, and matrix algebra, the book explains the key ideas at a relatively low technical level using real data examples. Each chapter also includes bibliographical notes and exercises. Real functional data sets from the text and MATLAB codes for analyzing the data examples are available for download from the author’s website.

Applied Functional Data Analysis

Author : J.O. Ramsay
Publisher : Springer
ISBN 13 : 0387224653
Total Pages : 191 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Applied Functional Data Analysis by : J.O. Ramsay

Download or read book Applied Functional Data Analysis written by J.O. Ramsay and published by Springer. This book was released on 2007-11-23 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.

Statistical Shape and Deformation Analysis

Author : Guoyan Zheng
Publisher : Academic Press
ISBN 13 : 0128104945
Total Pages : 508 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Statistical Shape and Deformation Analysis by : Guoyan Zheng

Download or read book Statistical Shape and Deformation Analysis written by Guoyan Zheng and published by Academic Press. This book was released on 2017-03-23 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Shape and Deformation Analysis: Methods, Implementation and Applications contributes enormously to solving different problems in patient care and physical anthropology, ranging from improved automatic registration and segmentation in medical image computing to the study of genetics, evolution and comparative form in physical anthropology and biology. This book gives a clear description of the concepts, methods, algorithms and techniques developed over the last three decades that is followed by examples of their implementation using open source software. Applications of statistical shape and deformation analysis are given for a wide variety of fields, including biometry, anthropology, medical image analysis and clinical practice. Presents an accessible introduction to the basic concepts, methods, algorithms and techniques in statistical shape and deformation analysis Includes implementation examples using open source software Covers real-life applications of statistical shape and deformation analysis methods

Introduction to Functional Data Analysis

Author : Piotr Kokoszka
Publisher : CRC Press
ISBN 13 : 1498746624
Total Pages : 307 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Introduction to Functional Data Analysis by : Piotr Kokoszka

Download or read book Introduction to Functional Data Analysis written by Piotr Kokoszka and published by CRC Press. This book was released on 2017-09-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

Object Oriented Data Analysis

Author : J. S. Marron
Publisher : CRC Press
ISBN 13 : 1351189662
Total Pages : 436 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Object Oriented Data Analysis by : J. S. Marron

Download or read book Object Oriented Data Analysis written by J. S. Marron and published by CRC Press. This book was released on 2021-11-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.

S+Functional Data Analysis

Author : Douglas B. Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 0387283935
Total Pages : 195 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis S+Functional Data Analysis by : Douglas B. Clarkson

Download or read book S+Functional Data Analysis written by Douglas B. Clarkson and published by Springer Science & Business Media. This book was released on 2006-06-02 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002). This user's manual also provides the documentation for the S+FDA library for SPlus.

Data Analysis Methods in Physical Oceanography

Author : Richard E. Thomson
Publisher : Elsevier
ISBN 13 : 0080477003
Total Pages : 654 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Data Analysis Methods in Physical Oceanography by : Richard E. Thomson

Download or read book Data Analysis Methods in Physical Oceanography written by Richard E. Thomson and published by Elsevier. This book was released on 2001-04-03 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Analysis Methods in Physical Oceanography is a practical referenceguide to established and modern data analysis techniques in earth and oceansciences. This second and revised edition is even more comprehensive with numerous updates, and an additional appendix on 'Convolution and Fourier transforms'. Intended for both students and established scientists, the fivemajor chapters of the book cover data acquisition and recording, dataprocessing and presentation, statistical methods and error handling,analysis of spatial data fields, and time series analysis methods. Chapter 5on time series analysis is a book in itself, spanning a wide diversity oftopics from stochastic processes and stationarity, coherence functions,Fourier analysis, tidal harmonic analysis, spectral and cross-spectralanalysis, wavelet and other related methods for processing nonstationarydata series, digital filters, and fractals. The seven appendices includeunit conversions, approximation methods and nondimensional numbers used ingeophysical fluid dynamics, presentations on convolution, statisticalterminology, and distribution functions, and a number of importantstatistical tables. Twenty pages are devoted to references. Featuring:• An in-depth presentation of modern techniques for the analysis of temporal and spatial data sets collected in oceanography, geophysics, and other disciplines in earth and ocean sciences.• A detailed overview of oceanographic instrumentation and sensors - old and new - used to collect oceanographic data.• 7 appendices especially applicable to earth and ocean sciences ranging from conversion of units, through statistical tables, to terminology and non-dimensional parameters. In praise of the first edition: "(...)This is a very practical guide to the various statistical analysis methods used for obtaining information from geophysical data, with particular reference to oceanography(...)The book provides both a text for advanced students of the geophysical sciences and a useful reference volume for researchers." Aslib Book Guide Vol 63, No. 9, 1998 "(...)This is an excellent book that I recommend highly and will definitely use for my own research and teaching." EOS Transactions, D.A. Jay, 1999 "(...)In summary, this book is the most comprehensive and practical source of information on data analysis methods available to the physical oceanographer. The reader gets the benefit of extremely broad coverage and an excellent set of examples drawn from geographical observations." Oceanography, Vol. 12, No. 3, A. Plueddemann, 1999 "(...)Data Analysis Methods in Physical Oceanography is highly recommended for a wide range of readers, from the relative novice to the experienced researcher. It would be appropriate for academic and special libraries." E-Streams, Vol. 2, No. 8, P. Mofjelf, August 1999

Density Estimation for Statistics and Data Analysis

Author : Bernard. W. Silverman
Publisher : Routledge
ISBN 13 : 1351456172
Total Pages : 176 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Density Estimation for Statistics and Data Analysis by : Bernard. W. Silverman

Download or read book Density Estimation for Statistics and Data Analysis written by Bernard. W. Silverman and published by Routledge. This book was released on 2018-02-19 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician. The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text. Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.

Elastic Shape Analysis of Three-Dimensional Objects

Author : Ian H. Jermyn
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681730286
Total Pages : 187 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Elastic Shape Analysis of Three-Dimensional Objects by : Ian H. Jermyn

Download or read book Elastic Shape Analysis of Three-Dimensional Objects written by Ian H. Jermyn and published by Morgan & Claypool Publishers. This book was released on 2017-09-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

Recent Advances in Functional Data Analysis and Related Topics

Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
ISBN 13 : 3790827363
Total Pages : 322 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis Recent Advances in Functional Data Analysis and Related Topics by : Frédéric Ferraty

Download or read book Recent Advances in Functional Data Analysis and Related Topics written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2011-06-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.

Spectral and Shape Analysis in Medical Imaging

Author : Martin Reuter
Publisher : Springer
ISBN 13 : 3319512374
Total Pages : 133 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Spectral and Shape Analysis in Medical Imaging by : Martin Reuter

Download or read book Spectral and Shape Analysis in Medical Imaging written by Martin Reuter and published by Springer. This book was released on 2016-12-10 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of the First International Workshop on Spectral and Shape Analysis in Medical Imaging, SeSAMI 2016, held in conjunction with MICCAI 2016, in Athens, Greece, in October 2016. The 10 submitted full papers presented in this volume were carefully reviewed. The papers reflect the following topics: spectral methods; longitudinal methods; and shape methods.

Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications

Author : Chiara Brombin
Publisher : Springer
ISBN 13 : 9783319263106
Total Pages : 115 pages
Book Rating : 4.2/5 (631 download)

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Book Synopsis Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications by : Chiara Brombin

Download or read book Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications written by Chiara Brombin and published by Springer. This book was released on 2016-02-19 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric tests. The models are simple to understand and interpret and provide a useful tool to describe the global dynamics of the landmark configurations. However, because of the non-Euclidean nature of shape spaces, distributions in shape spaces are not straightforward to obtain. The book explores the use of the Gaussian distribution in the configuration space, with similarity transformations integrated out. Specifically, it works with the offset-normal shape distribution as a probability model for statistical inference on a sample of a temporal sequence of landmark configurations. This enables inference for Gaussian processes from configurations onto the shape space. The book is divided in two parts, with the first three chapters covering material on the offset-normal shape distribution, and the remaining chapters covering the theory of NonParametric Combination (NPC) tests. The chapters offer a collection of applications which are bound together by the theme of this book. They refer to the analysis of data from the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions. For these data, it may be desirable to provide a description of the dynamics of the expressions, or testing whether there is a difference between the dynamics of two facial expressions or testing which of the landmarks are more informative in explaining the pattern of an expression.

Modern Data Analysis

Author : Robert L. Launer
Publisher : Academic Press
ISBN 13 : 1483263061
Total Pages : 216 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Modern Data Analysis by : Robert L. Launer

Download or read book Modern Data Analysis written by Robert L. Launer and published by Academic Press. This book was released on 2014-05-12 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Data Analysis contains the proceedings of a Workshop on Modern Data Analysis held in Raleigh, North Carolina, on June 2-4, 1980 under the auspices of the United States Army Research Office. The papers review theories and methods of data analysis and cover topics ranging from single and multiple quantile-quantile (Q-Q) plotting procedures to biplot display and pencil-and-paper exploratory data analysis methods. Projection pursuit methods for data analysis are also discussed. Comprised of nine chapters, this book begins with an introduction to styles of data analysis techniques, followed by an analysis of single and multiple Q-Q plotting procedures. Problems involving extreme-value data and the behavior of sample averages are considered. Subsequent chapters deal with the use of smelting in guiding re-expression; geometric data analysis; and influence functions and regression diagnostics. The final chapter examines the use and interpretation of robust analysis of variance for the general non-full-rank linear model. The procedures are described in terms of their mathematical structure, which leads to efficient computational algorithms. This monograph should be of interest to mathematicians and statisticians.