Springer Series in Statistics – serie

This second edition of a classic text offers an extensively revised and updated treatment of multivariate statistical analysis and its practical implementation using the LISREL program. In addition to core topics such as structural equation modeling, confirmatory and exploratory factor analyses, regression, principal component analysis, and longitudinal data analysis, it introduces two new chapters on models for twin data and simulation, and adds important new sections on time series analysis, mediation and moderation, interaction models, and multitrait-multimethod models. Combining statistical theory and methods with practical guidance, the book provides numerous illustrative examples from economics, psychology, sociology, meteorology, and genetics. Each example includes LISREL input and output, with detailed interpretations of results. The numerical algorithms used by LISREL for model estimation are also explained.Ideal for master’s and PhD students as well as researchers in the social, behavioral, economic, and related sciences, this volume can also serve as a comprehensive textbook for courses on multivariate statistical analysis.

This book describes the important ideas in a variety of fields such as medicine, biology, finance, and marketing in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of colour graphics. It is a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book.This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorisation, and spectral clustering. There is also a chapter on methods for "wide'' data (p bigger than n), including multiple testing and false discovery rates.

Sample data alone never suffice to draw conclusions about populations. Inference always requires assumptions about the population and sampling process. Statistical theory has revealed much about how strength of assumptions affects the precision of point estimates, but has had much less to say about how it affects the identification of population parameters. Indeed, it has been commonplace to think of identification as a binary event – a parameter is either identified or not – and to view point identification as a precondition for inference. Yet there is enormous scope for fruitful inference using data and assumptions that partially identify population parameters. This book explains why and shows how. The book presents in a rigorous and thorough manner the main elements of Charles Manski's research on partial identification of probability distributions. One focus is prediction with missing outcome or covariate data. Another is decomposition of finite mixtures, with application to the analysis of contaminated sampling and ecological inference. A third major focus is the analysis of treatment response. Whatever the particular subject under study, the presentation follows a common path. The author first specifies the sampling process generating the available data and asks what may be learned about population parameters using the empirical evidence alone. He then ask how the (typically) setvalued identification regions for these parameters shrink if various assumptions are imposed. The approach to inference that runs throughout the book is deliberately conservative and thoroughly nonparametric.

This is a book on bootstrap and related resampling methods for temporal and spatial data exhibiting various forms of dependence. Like the resam­ pling methods for independent data, these methods provide tools for sta­ tistical analysis of dependent data without requiring stringent structural assumptions. This is an important aspect of the resampling methods in the dependent case, as the problem of model misspecification is more preva­ lent under dependence and traditional statistical methods are often very sensitive to deviations from model assumptions. Following the tremendous success of Efron's (1979) bootstrap to provide answers to many complex problems involving independent data and following Singh's (1981) example on the inadequacy of the method under dependence, there have been several attempts in the literature to extend the bootstrap method to the dependent case. A breakthrough was achieved when resampling of single observations was replaced with block resampling, an idea that was put forward by Hall (1985), Carlstein (1986), Kiinsch (1989), Liu and Singh (1992), and others in various forms and in different inference problems. There has been a vig­ orous development in the area of res amp ling methods for dependent data since then and it is still an area of active research. This book describes various aspects of the theory and methodology of resampling methods for dependent data developed over the last two decades. There are mainly two target audiences for the book, with the level of exposition of the relevant parts tailored to each audience.

This book is an attempt to present a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. This framework allows us to view a vast assortment of simulation problems from a single unified perspective. It gives a great deal of insight into the fundamental nature of rare event simulation. Unfortunately, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. In this text, I have tried to keep the mathematical preliminaries to a minimum; the only prerequisite is a single large deviation theorem dealing with sequences of Rd­ valued random variables. (This theorem and a proof are given in the text.) Large deviation theory is a burgeoning area of probability theory and many of the results in it can be applied to simulation problems. Rather than try to be as complete as possible in the exposition of all possible aspects of the available theory, I have tried to concentrate on demonstrating the methodology and the principal ideas in a fairly simple setting. Madison, Wisconsin 2003 James Antonio Bucklew Contents 1. Random Number Generation . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1.1 Uniform Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Nonuniform Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 The Inversion Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 The Acceptance---Rejection Method . . . . . . . . . . . . 10 . . . . . 1.3 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . 13 . . . . . . . . . . . 1.3.1 Inversion by Truncation of a ContinuousAnalog. . . . . . 14 1.3.2 Acceptance---Rejection . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . .

Frederick Mosteller has inspired numerous statisticians and other scientists by his creative approach to statistics and its applications. This volume brings together 40 of his most original and influential papers, capturing the variety and depth of his writings. The editors hope to share these with a new generation of researchers, so that they can build upon his insights and efforts.This volume of selected papers is a companion to the earlier volume A Statistical Model: Frederick Mosteller's Contributions to Statistics, Science, and Public Policy, edited by Stephen E. Fienberg, David C. Hoaglin, William H. Kruskal, and Judith M. Tanur (Springer-Verlag, 1990), and to Mosteller's forthcoming autobiography, which will also be published by Springer-Verlag. It includes a biography and a comprehensive bibliography of Mosteller's books, papers, and other writings.Stephen E. Fienberg is Maurice Falk University Professor of Statistics and Social Science, in the Departments of Statistics and Machine Learning at Carnegie Mellon University, Pittsburgh, PA. David C. Hoaglin is Principal Scientist at Abt Associates Inc., Cambridge, MA.

This text is intended to provide a strong theoretical background in testing hypotheses and decision theory for those who will be practicing in the real worldorwhowillbeparticipatinginthetrainingofreal-worldstatisticiansand biostatisticians. In previous editions of this text, my rhetoric was somewhat tentative. I was saying, in e?ect, “Gee guys, permutation methods provide a practical real-world alternative to asymptotic parametric approximations. Why not give them a try?” But today, the theory, the software, and the hardware have come together. Distribution-free permutation procedures are the primary method for testing hypotheses. Parametric procedures and the bootstrap are to be reserved for the few situations in which they may be applicable. Four factors have forced this change: 1. Desire by workers in applied ?elds to use the most powerful statistic for their applications. Such workers may not be aware of the fundamental lemma of Neyman and Pearson, but they know that the statistic they wanttouse—acomplexscoreoraratioofscores,doesnothaveanalready well-tabulated distribution. 2. Pressure from regulatory agencies for the use of methods that yield exact signi?cance levels, not approximations. 3. A growing recognition that most real-world data are drawn from mixtures of populations. 4. A growing recognition that missing data is inevitable, balanced designs the exception. Thus, it seems natural that the theory of testing hypothesis and the more general decision theory in which it is embedded should be introduced via the permutation tests. On the other hand, certain relatively robust param- ric tests such as Student’s t continue to play an essential role in statistical practice.

For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution families—nonparametric, semiparametric and parametric—some well known and some not. An all-encompassing view is taken for the purpose of identifying relationships, origins and structures of the various families. A unified methodological approach for the introduction of parameters into families is developed, and the properties that the parameters imbue a distribution are clarified. These results provide essential tools for intelligent choice of models for data analysis. Many of the results given are new and have not previously appeared in print. This book provides a comprehensive reference for anyone working with nonnegative data.

Sustainability of pension systems, intergeneration fiscal equity under population aging, and accounting for health care benefits for future retirees are examples of problems that cannot be solved without understanding the nature of population forecasts and their uncertainty. Similarly, the accuracy of population estimates directly affects both the distributions of formula-based government allocations to sub-national units and the apportionment of political representation. The book develops the statistical foundation for addressing such issues. Areas covered include classical mathematical demography, event history methods, multi-state methods, stochastic population forecasting, sampling and census coverage, and decision theory. The methods are illustrated with empirical applications from Europe and the U.S.For statisticians the book provides a unique introduction to demographic problems in a familiar language. For demographers, actuaries, epidemiologists, and professionals in related fields, the book presents a unified statistical outlook on both classical methods of demography and recent developments. To facilitate its classroom use, exercises are included. Over half of the book is readily accessible to undergraduates, but more maturity may be required to benefit fully from the complete text. Knowledge of differential and integral calculus, matrix algebra, basic probability theory, and regression analysis is assumed.Juha M. Alho is Professor of Statistics, University of Joensuu, Finland, and Bruce D. Spencer is Professor of Statistics and Faculty Fellow at the Institute for Policy Research, Northwestern University. Both have contributed extensively to statistical demography and served in advisory roles and as statistical consultants in the field.

Sustainability of pension systems, intergeneration fiscal equity under population aging, and accounting for health care benefits for future retirees are examples of problems that cannot be solved without understanding the nature of population forecasts and their uncertainty. Similarly, the accuracy of population estimates directly affects both the distributions of formula-based government allocations to sub-national units and the apportionment of political representation. The book develops the statistical foundation for addressing such issues. Areas covered include classical mathematical demography, event history methods, multi-state methods, stochastic population forecasting, sampling and census coverage, and decision theory. The methods are illustrated with empirical applications from Europe and the U.S.For statisticians the book provides a unique introduction to demographic problems in a familiar language. For demographers, actuaries, epidemiologists, and professionals in related fields, the book presents a unified statistical outlook on both classical methods of demography and recent developments. To facilitate its classroom use, exercises are included. Over half of the book is readily accessible to undergraduates, but more maturity may be required to benefit fully from the complete text. Knowledge of differential and integral calculus, matrix algebra, basic probability theory, and regression analysis is assumed.Juha M. Alho is Professor of Statistics, University of Joensuu, Finland, and Bruce D. Spencer is Professor of Statistics and Faculty Fellow at the Institute for Policy Research, Northwestern University. Both have contributed extensively to statistical demography and served in advisory roles and as statistical consultants in the field.

This book provides a comprehensive treatment on modeling approaches for non-Gaussian repeated measures, possibly subject to incompleteness. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The text is organized so the reader can skip the software-oriented chapters and sections without breaking the logical flow.

Multidimensionalscaling(MDS)isatechniquefortheanalysisofsimilarity or dissimilarity data on a set of objects. Such data may be intercorrelations of test items, ratings of similarity on political candidates, or trade indices forasetofcountries.MDSattemptstomodelsuchdataasdistancesamong pointsinageometricspace.Themainreasonfordoingthisisthatonewants a graphical display of the structure of the data, one that is much easier to understand than an array of numbers and, moreover, one that displays the essential information in the data, smoothing out noise. There are numerous varieties of MDS. Some facets for distinguishing among them are the particular type of geometry into which one wants to mapthedata,themappingfunction,thealgorithmsusedto?ndanoptimal data representation, the treatment of statistical error in the models, or the possibility to represent not just one but several similarity matrices at the same time. Other facets relate to the di?erent purposes for which MDS has been used, to various ways of looking at or “interpreting” an MDS representation, or to di?erences in the data required for the particular models. Inthisbook,wegiveafairlycomprehensivepresentationofMDS.Forthe reader with applied interests only, the ?rst six chapters of Part I should be su?cient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.

Amongmanyexcitingdevelopmentsinstatisticsoverthelasttwodecades, nonlineartimeseriesanddata-analyticnonparametricmethodshavegreatly advanced along seemingly unrelated paths. In spite of the fact that the - plication of nonparametric techniques in time series can be traced back to the 1940s at least, there still exists healthy and justi?ed skepticism about the capability of nonparametric methods in time series analysis. As - thusiastic explorers of the modern nonparametric toolkit, we feel obliged to assemble together in one place the newly developed relevant techniques. Theaimofthisbookistoadvocatethosemodernnonparametrictechniques that have proven useful for analyzing real time series data, and to provoke further research in both methodology and theory for nonparametric time series analysis. Modern computers and the information age bring us opportunities with challenges. Technological inventions have led to the explosion in data c- lection (e.g., daily grocery sales, stock market trading, microarray data). The Internet makes big data warehouses readily accessible. Although cl- sic parametric models, which postulate global structures for underlying systems, are still very useful, large data sets prompt the search for more re?nedstructures,whichleadstobetterunderstandingandapproximations of the real world. Beyond postulated parametric models, there are in?nite other possibilities. Nonparametric techniques provide useful exploratory tools for this venture, including the suggestion of new parametric models and the validation of existing ones.

This book presents knowledge gained by the authors along with methods they developed, over more than 30 years of experience measuring, mod- ing, and mapping environmental space–time ?elds. That experience embraces both large (continentwide) spatial domains and small. In part it comes from their research, working with students as well as coinvestigators. But much was gained from all sorts of interactions with many individuals who have had to contend with the challenges these ?elds present. They include statistical as well as subject area scientists, in areas as diverse as analytical chemistry, airsampling,atmosphericscience,environmentalepidemiology,environmental risk management, and occupational health among others. We have colla- rated and consulted with government scientists as well as policy-makers, in all,alargegroupofindividualsfromwhomwehavelearnedalotandtowhom we are indebted. We hope all in these diverse groups will ?nd something of value in this book. We believe it will also bene?t graduate students, both in statistics and subject areas who must deal with the analysis of environmental ?elds. In fact we have given a successful statistics graduate course based on it. The book (and course) re?ect our conviction about the need for statistical scientiststolearnaboutthephenomenatheypurporttoexplain. Totheextent feasible, we have covered important nonstatistical issues involved in dealing with environmental processes. Thus in writing the book we have tried to strike a balance between important qualitative and quantitative aspects of the subject. Much of the most technical statistical-mathematical material has been placed in the starred sections, chapters, and appendices.

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions.With 116 examples, 54 figures, and 167 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. The revised second edition includes new sections on extreme value copulas, tail dependence, and quasi-copulas.

Since its inception by Perron and Frobenius, the theory of non-negative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its development is still proceeding rapidly as a branch of pure mathematics in its own right. While there are books which cover this or that aspect of the theory, it is nevertheless not uncommon for workers in one or another branch of its development to be unaware of what is known in other branches, even though there is often formal overlap. One of the purposes of this book is to relate several aspects of the theory, insofar as this is possible. The author hopes that the book will be useful to mathematicians; but in particular to the workers in applied fields, so the mathematics has been kept as simple as could be managed. The mathematical requisites for reading it are: some knowledge of real-variable theory, and matrix theory; and a little knowledge of complex-variable; the emphasis is on real-variable methods. (There is only one part of the book, the second part of 55.5, which is of rather specialist interest, and requires deeper knowledge.) Appendices provide brief expositions of those areas of mathematics needed which may be less g- erally known to the average reader.

Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. This book starts from theoretical foundations including functional nonparametric modeling, description of the mathematical framework, construction of the statistical methods, and statements of their asymptotic behaviors. It proceeds to computational issues including R and S-PLUS routines. Several functional datasets in chemometrics, econometrics, and pattern recognition are used to emphasize the wide scope of nonparametric functional data analysis in applied sciences. The companion Web site includes R and S-PLUS routines, command lines for reproducing examples presented in the book, and the functional datasets.Rather than set application against theory, this book is really an interface of these two features of statistics. A special effort has been made in writing this book to accommodate several levels of reading. The computational aspects are oriented toward practitioners whereas open problems emerging from this new field of statistics will attract Ph.D. students and academic researchers. Finally, this book is also accessible to graduate students starting in the area of functional statistics.

Over the last few decades, important progresses in the methods of sampling have been achieved. This book draws up an inventory of new methods that can be useful for selecting samples. Forty-six sampling methods are described in the framework of general theory. The algorithms are described rigorously, which allows implementing directly the described methods. This book is aimed at experienced statisticians who are familiar with the theory of survey sampling.

Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Factorial experiments are often used in case studies in quality management and Design for Six Sigma (DFSS). The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. The present book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. In order to equip the readers with the necessary background, some foundational concepts and results are developed in Chapter 2. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design. It can also be used for courses in combinatorial designs or combinatorial mathematics.

Missing data arise in almost all scientific disciplines. In many cases, the treatment of missing data in an analysis is carried out in a casual and ad-hoc manner, leading, in many cases, to invalid inference and erroneous conclusions. In the past 20 years or so, there has been a serious attempt to understand the underlying issues and difficulties that come about from missing data and their impact on subsequent analysis. There has been a great deal written on the theory developed for analyzing missing data for finite-dimensional parametric models. This includes an extensive literature on likelihood-based methods and multiple imputation. More recently, there has been increasing interest in semiparametric models which, roughly speaking, are models that include both a parametric and nonparametric component. Such models are popular because estimators in such models are more robust than in traditional parametric models. The theory of missing data applied to semiparametric models is scattered throughout the literature with no thorough comprehensive treatment of the subject.This book combines much of what is known in regard to the theory of estimation for semiparametric models with missing data in an organized and comprehensive manner. It starts with the study of semiparametric methods when there are no missing data. The description of the theory of estimation for semiparametric models is at a level that is both rigorous and intuitive, relying on geometric ideas to reinforce the intuition and understanding of the theory. These methods are then applied to problems with missing, censored, and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.

The prerequisite for reading this text is a calculus based course in Probability and Mathematical Statistics, along with the usual curricularmathematical requi- ments for every science major. For graduate students from disciplines other than mathematical sciences much advantage, viz., both insight and mathematical - turity, is gained by having had experience quantifying the assurance for safety of structures, operability of systems or health of persons. It is presumed that each student will have some familiarity with Mathematica or Maple or better yet also have available some survival analysis software such as S Plus or R, to handle the computations with the data sets. This material has been selected under the conviction that the most practical aid any investigator can have is a good theory. The course is intended for p- sons who will, during their professional life, be concerned with the 'theoretical' aspects of applied science. This implies consulting with industrial mathema- cians/statisticians' lead engineers in various fields, physcists, chemists, material scientists and other technical specialists who are collaborating to solve some d- ficult technological/scientific problem. Accordingly, there are sections devoted to the deportment of applied mathematicians during consulting. This corresponds to the 'bedside manner' of physicians and is a important aspect of professionalism.

Geostatistics is concerned with estimation and prediction problems for spatially continuous phenomena, using data obtained at a limited number of spatial locations. The name reflects its origins in mineral exploration, but the methods are now used in a wide range of settings including public health and the physical and environmental sciences. Model-based geostatistics refers to the application of general statistical principles of modeling and inference to geostatistical problems. This volume is the first book-length treatment of model-based geostatistics.The authors have written an expository text, emphasizing statistical methods and applications rather than the underlying mathematical theory. Analyses of datasets from a range of scientific contexts feature prominently, and simulations are used to illustrate theoretical results. Readers can reproduce most of the computational results in the book by using the authors' R-based software package, geoR, whose usage is illustrated in a computation section at the end of each chapter.The book assumes a working knowledge of classical and Bayesian methods of inference, linear models, and generalized linear models, but does not require previous exposure to spatial statistical models or methods. The authors have used the material in MSc-level statistics courses.

The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book reviews these techniques and covers advances in the field. This is the first book to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. Focusing mainly on Bayesian inference, the author reviews several frequentist techniques, especially selecting the number of components of a finite mixture model, and discusses some of their shortcomings compared to the Bayesian approach. The book is designed to show how finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, the book will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

Stochastic ordering is a fundamental guide for decision making under uncertainty. It is also an essential tool in the study of structural properties of complex stochastic systems. This reference text presents a comprehensive coverage of the various notions of stochastic orderings, their closure properties, and their applications. Some of these orderings are routinely used in many applications in economics, finance, insurance, management science, operations research, statistics, and various other fields of study. And the value of the other notions of stochastic orderings still needs to be explored further.This book is an ideal reference for anyone interested in decision making under uncertainty and interested in the analysis of complex stochastic systems. It is suitable as a text for advanced graduate course on stochastic ordering and applications.

Scientists and others today often collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data.  Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modeling, 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, much of it based on the authors’ own research work, while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields.  This second edition is aimed at a wider range of readers, and especially those who would like to apply these techniques to their research problems. It complements the authors' other volume Applied Functional Data Analysis: Methods and Case Studies. In particular, there is an extended coverage of data smoothing and other matters arising in the preliminaries to a functional data analysis. The chapters on the functional linear model and modeling of the dynamics of systems through the use of differential equations and principal differential analysis have been completely rewritten and extended to include new developments. Other chapters have been revised substantially, often to give more weight to examples and practical considerations.

Statistical Tools for Nonlinear Regression, Second Edition, presents methods for analyzing data using parametric nonlinear regression models. The new edition has been expanded to include binomial, multinomial and Poisson non-linear models. Using examples from experiments in agronomy and biochemistry, it shows how to apply these methods. It concentrates on presenting the methods in an intuitive way rather than developing the theoretical backgrounds. The examples are analyzed with the free software nls2 updated to deal with the new models included in the second edition. The nls2 package is implemented in S-PLUS and R. Its main advantages are to make the model building, estimation and validation tasks, easy to do. More precisely, Complex models can be easily described using a symbolic syntax. The regression function as well as the variance function can be defined explicitly as functions of independent variables and of unknown parameters or they can be defined as the solution to a system of differential equations. Moreover, constraints on the parameters can easily be added to the model. It is thus possible to test nested hypotheses and to compare several data sets. Several additional tools are included in the package for calculating confidence regions for functions of parameters or calibration intervals, using classical methodology or bootstrap. Some graphical tools are proposed for visualizing the fitted curves, the residuals, the confidence regions, and the numerical estimation procedure.

This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.

Hidden Markov models have become a widely used class of statistical models with applications in diverse areas such as communications engineering, bioinformatics, finance and many more. This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states.In a unified way the book covers both models with finite state spaces, which allow for exact algorithms for filtering, estimation etc. and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Simulation in hidden Markov models is addressed in five different chapters that cover both Markov chain Monte Carlo and sequential Monte Carlo approaches. Many examples illustrate the algorithms and theory. The book also carefully treats Gaussian linear state-space models and their extensions and it contains a chapter on general Markov chain theory and probabilistic aspects of hidden Markov models.This volume will suit anybody with an interest in inference for stochastic processes, and it will be useful for researchers and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The algorithmic parts of the book do not require an advanced mathematical background, while the more theoretical parts require knowledge of probability theory at the measure-theoretical level.From the reviews:"By providing an overall survey of results obtained so far in a very readable manner, and also presenting some new ideas, this well-written book will appeal to academic researchers in the field of HMMs, with PhD students working on related topics included. It will also appeal to practitioners and researchers from other fields by guiding them through the computational steps needed for making inference HMMs and/or by providing them with the relevant underlying statistical theory. In the reviewer's opinion this book will shortly become a reference work in its field." MathSciNet"This monograph is a valuable resource. It provides a good literature review, an excellent account of the state of the art research on the necessary theory and algorithms, and ample illustrations of numerous applications of HMM. It goes much beyond the earlier resources on HMM...I anticipate this work to serve well many Technometrics readers in the coming years." Haikady N. Nagaraja for Technometrics, November 2006

This is the second volume of a text on the theory and practice of maximum penalized likelihood estimation. It is intended for graduate students in s- tistics, operationsresearch, andappliedmathematics, aswellasresearchers and practitioners in the ?eld. The present volume was supposed to have a short chapter on nonparametric regression but was intended to deal mainly with inverse problems. However, the chapter on nonparametric regression kept growing to the point where it is now the only topic covered. Perhaps there will be a Volume III. It might even deal with inverse problems. But for now we are happy to have ?nished Volume II. The emphasis in this volume is on smoothing splines of arbitrary order, but other estimators (kernels, local and global polynomials) pass review as well. We study smoothing splines and local polynomials in the context of reproducing kernel Hilbert spaces. The connection between smoothing splines and reproducing kernels is of course well-known. The new twist is thatlettingtheinnerproductdependonthesmoothingparameteropensup new possibilities: It leads to asymptotically equivalent reproducing kernel estimators (without quali?cations) and thence, via uniform error bounds for kernel estimators, to uniform error bounds for smoothing splines and, via strong approximations, to con?dence bands for the unknown regression function. ItcameassomewhatofasurprisethatreproducingkernelHilbert space ideas also proved useful in the study of local polynomial estimators.