Oxford Statistical Science Series – serie

Goodness of fit describes the validity of models involving statistical distribution of data, and smooth tests are a subset of these tests which are easy to apply and can be used in any situation in which there are relatively large sample sizes. Both concepts have become increasingly important with the advent of high-speed computers and the implementation of more complex models in the areas of probability and statistics. Written to be accessible to undergraduates with a working knowledge of statistics and calculus, this is an introductory reference work that should appeal to all professionals involved in statistical modelling.

This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.

This second edition of Models for Repeated Measurements has been comprehensively revised and updated, taking into account the huge amount of research that has been carried out in the subject in recent years. A wide variety of useful new models is now available, models that have revolutionized the analysis of such data. The second edition contains three new chapters on models for continuous non-normal data, on various design issues specific to repeated measurements, and on missing data and dropouts. Exercises have been added at the ends of most chapters, and the programming functions needed to carry out the analyses in the book are publicly available. Models for Repeated Measurements is an essential reference for research statisticians in agriculture, medicine, economics, and psychology, and for the many consulting statisticians who want an up-to-date expository account of this important topic. The book is organized into four parts. In the first part, the general context of repeated measurements is presented. The three basic types of response variables, continuous (normal), categorical and count, and duration, are introduced. There is a discussion of the ways in which such repeated observations are interdependent. The book also develops a framework for constructing suitable models, with the introduction of the necessary concepts of multivariate distributions and stochastic processes. In the following three parts, a large number of specific examples, including data tables, is presented to illustrate the models available. Each of these parts corresponds to one of the types of responses mentioned above. FROM REVIEWS OF THE FIRST EDITION . . . a timely book . . . useful both as a graduate text and as a consulting source. Statistical Methods in Medical Research

This book provides an introduction to the modern theory of likelihood-based statistical inference. This theory is characterized by several important features. One is the recognition that it is desirable to condition on relevant ancillary statistics. Another is that probability approximations are based on saddlepoint and closely related approximations that generally have very high accuracy. A third aspect is that, for models with nuisance parameters, inference is often based on marginal or conditional likelihoods, or approximations to these likelihoods. These methods have been shown often to yield substantial improvements over classical methods. The book also provides an up-to-date account of recent results in the field, which has been undergoing rapid development.

Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which, when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a numberof modifications to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specifically original. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user's perspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction

Over recent years, developments in statistical computing have freed statisticians from the burden of calculation and have made possible new methods of analysis that previously would have been too difficult or time-consuming. Up till now these developments have been primarily in numerical computation and graphical display, but equal steps forward are now being made in the area of symbolic computing, or in other words the use of computer languages and procedures to manipulate expressions. This allows researchers to compute an algebraic expression, rather than evaluate the expression numerically over a given range. This book summarizes a decade of research into the use of symbolic computation applied to statistical inference problems. It shows the considerable potential of the subject to automate statistical calculation, leaving researchers free to concentrate on new concepts. Starting with the development of algorithms applied to standard undergraduate problems, the book then goes on to develop increasingly more powerful tools. Later chapters then discuss the application of these algorithms to different areas of statistical methodology.

This book is an introduction to the principles and methodology of modern multivariate statistical analysis. It is written for the user and potential user of multivariate techniques as well as for students coming to the subject for the first time. The author's emphasis is problem-orientated and he is at pains to stress geometrical intuition in preference to algebraic manipulation. Mathematical sections that are not essential for a practical understanding of the techniques are clearly indicated so that they may be skipped by the non-specialist. Discrete and mixed variable techniques are presented as well as continuous variable techniques to give a comprehensive coverage of the subject. This updated edition includes a new appendix which traces developments that have taken place in the years since the publication of the first edition and which clarifies some issues raised by readers of the original text. References to about 60 recent books and articles supplement the material in this appendix. Overall, this volume provides an up-to-date and readable practical account of the subject, both for students of statistics and for research workers in subjects as diverse as anthropology, education, industry, medicine and taxonomy. The new edition includes a survey of the most recent developments in the subject.

This text provides an introduction to the use of nonlinear models in medical statistics, It is a practical text rather than a theoretical one and assumes a basic knowledge in statistical modelling and of generalized linear models. The book first provides a general introduction to nonlinear models, comparing them to generalized linear models. It describes data handling and formula definition and summarises the principal types of nonlinear regression formulae. there is an emphasis on techniques for non-normal data.Following chapters provide detailed examples of applications in various areas of medicine, epidemiology, clinical trials, quality of life, pharmokinetics, pharmacodynamics, assays and formulations, and molecular genetics.The book concludes with appendicies describing data handling and model formulae in more detail, and given ways of modelling dependencies in repeated measurements, and data for the exercises.

The use of clinical and laboratory information to detect conditions and predict patient outcomes is a mainstay of medical practice. Modern biotechnology offers increasing potential to develop sophisticated tests for these purposes. This book describes the statistical concepts and techniques for evaluating the accuracy of medical tests. Worked examples include applications to cancer biomarker studies, prospective disease screening studies, diagnostic radiology studies and audiology testing studies. The statistical methodology can be broadly applied for evaluating classifiers and to problems beyond medical settings.Several measures for quantifying test accuracy are described including the Receiver Operating Characteristic Curve. Pepe presents statistical procedures for the estimation and comparison of those measures among tests. Regression frameworks for assessing factors that influence test accuracy and for comparing tests while adjusting for such factors are presented. The sequence of research steps involved in the development of a test is considered in some detail. Sample size calculations and other issues pertinent to study design are described for tests at various phases of development. In addition, the impacts of missing data and imperfect reference data are addressed. These problems often occur in practice, and modern statistical procedures for dealing with them are discussed. Additional topics that are covered include: meta-analysis for summarizing the results of multiple studies of a test; the evaluation of markers for predicting event time data; and procedures for combining the results of multiple tests to improve classification.This book should be of interest to quantitative researchers and practicing statisticians. The book also covers the theoretical foundations for statistical inference and should therefore be of interest to academic statisticians including those involved in statistical methodological research in this field.

Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. The name derives from the Greek myth where Procrustes invited passers-by in for a pleasant meal and a night's rest on a magical bed that would exactly fit any guest. He then either stretched the guest on the rack or cut off their legs to make them fit perfectly into the bed. Theseus turned the tables on Procrustes, fatally adjusting him to fit his own bed.This text, the first monograph on Procrustes methods, unifies several strands in the literature and contains much new material. It focuses on matching two or more configurations by using orthogonal, projection and oblique axes transformations. Group-average summaries play an important part and links with other group-average methods are discussed. This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specifically original. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user's perspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction 29. Christopher G. Small and Jinfang Wang: Numerical Methods for Nonlinear Estimating Equations

The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory of graphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The statistical theory of log-linear and graphical models for contingency tables, covariance selection models, and graphical models with mixed discrete-continous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are described briefly, and appendices give details of the multivarate normal distribution and of the theory of regular exponential families. The author has recently been awarded the RSS Guy Medal in Silver 1996 for his innovative contributions to statistical theory and practice, and especially for his work on graphical models.

Time series analysis is one of several branches of statistics whose practical importance has increased with the availability of powerful computing tools. Methodology originally developed for specialized applications, for example in business forecasting or geophysical signal processing, is now widely available in general statistical packages. These computing developments have helped to bring the subject closer to the mainstream of applied statistics. This book is an introductory account of time-series analysis, written from the perspective of an applied statistician with a particular interest in biological applications. Separate chapters cover exploratory methods, the theory of stationary random processes, spectral analysis, repeated measurements, ARIMA modelling, forecasting, and bivariate time-series analysis. Throughout, analyses of data-sets drawn from the biological and medical sciences are integrated with the methodological development. The book is unique in its emphasis on biological and medical applications of time-series analysis. Nevertheless, its methodological content is more widely applicable, and it should be useful to both students and practitioners of applied statistics, whatever their specialization.

This volume comprises a comprehensive collection of original papers on the subject of estimating functions. It is intended to provide statisticians with an overview of both the theory and the applications of estimating functions in biostatistics, stochastic processes, and survey sampling. From the early 1960s when the concept of optimality criterion was first formulated, together with later work on optimal estimating functions, this subject has become both an active research area in its own right and also a corner-stone of the modern theory of statistics.Individual chapters have been written by experts in their respective fields and as a result this volume will be an invaluable reference guide to this topic as well as providing an introduction to the area for non-experts.

The book starts with a range of examples and develops techniques progressively, starting with standard least squares prediction of a single variable from another and moving onto shrinkage techniques for multiple variables. Chapters 6 and 7 refer mostly to methods that have been specifically developed for spectroscopy. The other chapters are quite general in their applicability. Likelihood and Bayesian inference features strongly, the latter allowing flexible analysis of a wide range of multivariate regression problems. The last chapter presents some Bayesian approaches to pattern recognition.For teaching purposes instructors may find particular chapters sufficiently self contained to recommend in isolation as reference or reading material. For example chapter 4 gives an in depth development of a range of shrinkage techniques. including partial least squares regression, ridge regression and principal components regression; together with discussion of the recently proposed continuum regression. Chapter 8 on pattern recognition may also be of us by itself in courses on multivariate analysis and Bayesian Statistics.

A well-designed experiment is an efficient method of learning about the world. Because experiments in the field and in the laboratory cannot avoid random error, statistical methods are essential for their efficient design and analysis. In this book, the fundamentals of optimum experimental design theory are presented. In the first part of the part of the book, the advantages of a statistical approach to the design of experiments are discussed, and the ideas of models, least squares fitting, and optimum experimental designs are introduced. The second part presents a more detailed discussion of the general theory of optimum design and an evaluation of various criteria that may be appropriate for designing experiments. Specific experiments are detailed and algorithms for the construction of designs are given.Each chapter is a self-contained topic, illustrated with examples drawn from science and engineering. Little previous statistical knowledge is assumed, and the derivation of mathematical results has been avoided. This book should be of interest to everyone concerned with designing efficient experiments in the laboratory or in the industry.

The principal aim of the book is an exposition of methods for the analysis of clustered observations; the secondary one is to provide substantive interest as a measure of uncertainty, quality, equity, or generally, as a summary of differences among experimental or observational units. Another goal is to make a balanced presentation of the advantages and limitations of these methodsThe examples used for illustration of methods are not drawn exclusively from the social sciences. Although models are motivated mainly by social science problems, they are applicable in a variety of situations involving (imperfect) replication, such as repeated measurements, repeated experiments, logitudinal analysis, and analysis of covariance structures in general.

Although introduced more than 60 years ago it is only during the last 15 years that there has been a systematic development of saddlepoint approximations. These approximations give a highly accurate expression for the tail of a distribution, not only in the centre of the distribution but also for very small tail probabilities. The price for this is a more cumbersome formula, the evaluation of which sometimes requires the use of a small personal computer. This book explains the ideas behind the saddlepoint approximations as well as giving a detailed mathematical description of the subject. The emphasis is two- fold. One is on popularizing the formulae through many worked out and ready to use examples. The second is on giving a comprehensive mathematical background for further research in the field. Some of the major subjects treated are uniformity of the approximations, tests in exponential families, and compound sums with applications in insurance mathematics.

The analysis of time series data has for many years been a central component of statistical research and practice and the theory of linear time series is now well-established. However, the theory of non-linear time series is still a rapidly developing subject. This book is an introduction to some of these developments and the present state of research. It is a theme of this book that developments in the study of dynamical systems have motivated many of the advances covered here. Consequently, Professor Tong discusses in some detail the fundamental concepts of dynamical systems theory such as limit cycles, Lyapunov exponents, thresholds, and stability, and demonstrates their role in the analysis of non-linear time series. The result is a book which provides the first accessible and comprehensive account of these exciting new developments and bridges the gap between linear and chaotic time series analysis. Both statisticians and dynamical system theorists will benefit from this account of the interplay between their subjects and the author has included discussions of many of the outstanding open problems which remain. As a companion to this book, a microcomputer software package is available for the testing for nonlinearity and the fitting of threshold autoregressive models. For more information, please contact the author.

Categorical data analysis is a special area of generalised linear models, which has become the most important area of statistical applications in many disciplines, from medicine to social sciences. This text presents the standard models and many newly developed ones in a language which can be immediately applied in many modern statistical packages such as GLIM, GENSTAT, S-Plus, as well as SAS and LISP-STAT. The book is structure around the distinction between independent events occurring to different individuals, resulting in frequencies, and repeated events occurring to the same individuals, yielding counts. The book demonstates that much of modern statistics can be seen as special cases of categorical data models; both generalized linear models and proportional hazards models can be fitted as log linear models. More specialized topics such as Markov chains, overdispersion and random effects, are also covered.

The book describes the use of smoothing techniques in statistics, including both density estimation and nonparametric regression. Considerable advances in research in this area have been made in recent years. The aim of this text is to describe a variety of ways in which these methods can be applied to practical problems in statistics. The role of smoothing techniques in exploring data graphically is emphasised, but the use of nonparametric curves in drawing conclusions from data, as an extension of more standard parametric models, is also a major focus of the book. Examples are drawn from a wide range of applications. The book is intended for those who seek an introduction to the area, with an emphasis on applications rather than on detailed theory. It is therefore expected that the book will benefit those attending courses at an advanced undergraduate, or postgraduate, level, as well as researchers, both from statistics and from other disciplines, who wish to learn about and apply these techniques in practical data analysis. The text makes extensive reference to S-Plus, as a computing environment in which examples can be explored. S-Plus functions and example scripts are provided to implement many of the techniques described. These parts are, however, clearly separate from the main body of text, and can therefore easily be skipped by readers not interested in S-Plus.

This new edition of the successful multi-disciplinary text Statistical Modelling in GLIM takes into account new developments in both statistical software and statistical modelling. Including three new chapters on mixture and random effects models, it provides a comprehensive treatment of the theory of statistical modelling with generalised linear models with an emphasis on applications to practical problems and an expanded discussion of statistical theory. A wide range of case studies is also provided, using the normal, binomial, Poisson, multinomial, gamma, exponential and Weibull distributions.This book is ideal for graduates and research students in applied statistics and a wide range of quantitative disciplines, including biology, medicine and the social sciences. Professional statisticians at all levels will also find it an invaluable desktop companion.

The first edition of Analysis for Longitudinal Data has become a classic. Describing the statistical models and methods for the analysis of longitudinal data, it covers both the underlying statistical theory of each method, and its application to a range of examples from the agricultural and biomedical sciences. The main topics discussed are design issues, exploratory methods of analysis, linear models for continuous data, general linear models for discrete data, and models and methods for handling data and missing values. Under each heading, worked examples are presented in parallel with the methodological development, and sufficient detail is given to enable the reader to reproduce the author's results using the data-sets as an appendix. This new edition of Analysis for Longitudinal Data provides a thorough and expanded revision of this important text. It includes two new chapters; the first discusses fully parametric models for discrete repeated measures data, and the second explores statistical models for time-dependent predictors.

`Repression diagnostics are a collection of methods used to find (diagnose) unusual features in a regression problem.`Although informal diagnostics have a long and respectable history, it is only in the last fifteen years or so that they have been systematically studied. Atkinson has been one of the key players in this area, with several important papers dating from the early 1970s. The book clearly builds on much of that earlier work, but it is not intended as a research monograph, but as an introduction and guide to using diagnostics as a practical part of regression analysis. Both research statisticians and users of statistics should find this book generally both interesting and accessible.`A major strength of this book is Atkinson's decision to present only a subset of diagnostic methods that have been suggested in the literature, rather than giving the reader a menu of possibilities to choose from. In a field with few underlying principles and much that requires experience and practice, the reader who is new to the area can only benefit from learning a reasonably coherent collection of methods.' From a review by Sanford Weisberg, University of Minnesota.

This is a practical text for those who wish to analyse data from Reliability studies. The emphasis is on clear explanation of the techniques used, supported by extensive mathematical and statistical background and nature of the data before it is analysed. There are chapters on survival analysis, using illuminating case studies.

This book describes statistical techniques for the design and evaluation of research studies on medical diagnostic tests, screening tests, biomarkers and new technologies for classification and prediction in medicine.Readership: Researchers and students in biostatistics (medical statistics), statistics, medical science, public health and clinical research.

Sir David Cox is among the most important statisticians of the past half-century. He has made pioneering and highly influential contributions to a uniquely wide range of topics in statistics and applied probability. His teaching has inspired generations of students, and many well-known researchers have begun as his graduate students or have worked with him at early stages of their careers. Legions of others have been stimulated and enlightened by the clear, concise, and direct exposition exemplified by his many books, papers, and lectures. This book presents a collection of chapters by major statistical researchers who attended a conference held at the University of Neuchatel in July 2004 to celebrate David Cox's 80th birthday. Each chapter is carefully crafted and collectively present current developments across a wide range of research areas from epidemiology, environmental science, finance, computing and medicine. Edited by Anthony Davison, Ecole Polytechnique Federale de Lausanne, Switzerland; Yadolah Dodge, University of Neuchatel, Switzerland; and N. Wermuth, Goteborg University, Sweden, with chapters by Ole E. Barndorff-Nielsen, Sarah C. Darby, Christina Davies, Peter J. Diggle, David Firth, Peter Hall, Valerie S. Isham, Kung-Yee Liang, Peter McCullagh, Paul McGale, Amilcare Porporato, Nancy Reid, Brian D. Ripley, Ignacio Rodriguez-Iturbe, Andrea Rotnitzky, Neil Shephard, Scott L. Zeger, and including a brief biography of David Cox, this book is suitable for students of statistics, epidemiology, environmental science, finance, computing and medicine, and academic and practising statisticians.

This text brings together important ideas on the model-based approach to sample survey, which has been developed over the last twenty years. Suitable for graduate students and professional statisticians, it moves from basic ideas fundamental to sampling to more rigorous mathematical modelling and data analysis and includes exercises and solutions.

The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables.This new and extended edition of Graphical Models provides the basic mathematical and statistical theory of graphical models, incorporating the many advances that have been made in the field since the publication of the first edition in 1996. Lauritzen discusses basic graph theory and the fundamentals of conditional independence both in abstract form for conditional independence based on graphs and for probabilistic conditional independence. The associated Markov theory, forming the basis of all models in the book, is treated in some detail. The statistical theory based on likelihood methods and conjugate Bayesian analysis is developed for log-linear and Gaussian graphical models, as well as for graphical models involving mixed discrete and continuous data. A new and important chapter is devoted to structure estimation because this has become a dominating part of modern developments. Causal interpretation of models based on directed acyclic graphs and chain graphs are also discussed.The appendices contain some of the general mathematical results needed as background for the main contents of the book, including basic measure theory and the theory of Markov kernels, convex optimization, properties of the multivariate Gaussian distributions and derived distributions, as well as a brief exposition of the theory of exponential families.

Time series analysis is one of several branches of statistics whose practical importance has increased with the availability of powerful computational tools. Methodology that was originally developed for specialized applications, for example in finance or geophysics, is now widely available within general statistical packages. The second edition of Time Series: A Biostatistical Introduction is an introductory account of time series analysis, written from the perspective of applied statisticians whose interests lie primarily in the biomedical and health sciences. This edition has a stronger focus on substantive applications, in which each statistical analysis is directed at a specific research question. Separate chapters cover simple descriptive methods of analysis, including time-plots, smoothing, the correlogram and the periodogram; theory of stationary random processes; discrete-time models for single series; continuous-time models for single series; generalized linear models for time series of counts; models for replicated series; spectral analysis, and bivariate time series.The book is unique in its focus on biomedical and health science applications, which has been strengthened in this second edition. Nevertheless, the methods described are more widely applicable. It should be useful to teachers and students on masters-level degree courses in statistics, biostatistics and epidemiology, and to biomedical and health scientists with a knowledge of statistical methods at undergraduate level. Throughout, examples based on real datasets show a close interplay between statistical method and substantive science. This book will also describe the implementation of the methods in the R computing environment and provide access to R code and datasets.