Springer Series in Statistics – serie

This major new edition features many topics not covered in the original, including graphical models, random forests, and ensemble methods. As before, it covers the conceptual framework for statistical data in our rapidly expanding computerized world.

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 book gives a detailed account of bootstrap methods and their properties for dependent data, covering a wide range of topics such as block bootstrap methods, bootstrap methods in the frequency domain, resampling methods for long range dependent data, and resampling methods for spatial data. The first five chapters of the book treat the theory and applications of block bootstrap methods at the level of a graduate text. The rest of the book is written as a research monograph, with frequent references to the literature, but mostly at a level accessible to graduate students familiar with basic concepts in statistics. Supplemental background material is added in the discussion of such important issues as second order properties of bootstrap methods, bootstrap under long range dependence, and bootstrap for extremes and heavy tailed dependent data. Further, illustrative numerical examples are given all through the book and issues involving application of the methodology are discussed.The book fills a gap in the literature covering research on resampling methods for dependent data that has witnessed vigorous growth over the last two decades but remains scattered in various statistics and econometrics journals. It can be used as a graduate level text for a special topics course on resampling methods for dependent data and also as a research monograph for statisticians and econometricians who want to learn more about the topic and want to apply the methods in their own research. S.N. Lahiri is a professor of Statistics at the Iowa State University, is a Fellow of the Institute of Mathematical Statistics and a Fellow of the American Statistical Association.

This book presents 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 perspective allows us to view a vast assortment of simulation problems from a unified single perspective. It gives a great deal of insight into the fundamental nature of rare event simulation.Until now, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. This text keeps the mathematical preliminaries to a minimum with the only prerequisite being a single large deviation theory result that is given and proved 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, the book concentrates on demonstrating the methodology and the principal ideas in a fairly simple setting.The book contains over 50 figures and detailed simulation case studies covering a wide variety of application areas including statistics, telecommunications, and queueing systems.James A. Bucklew holds the rank of Professor with appointments in the Department of Electrical and Computer Engineering and in the Department of Mathematics at the University of Wisconsin-Madison. He is the author of "Large Deviation Techniques in Decision, Simulation, and Estimation".

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. The authors begin with models for the full marginal distribution of the outcome vector. This allows model fitting to be based on maximum likelihood principles, immediately implying inferential tools for all parameters in the models. At the same time, they formulate computationally less complex alternatives, including generalized estimating equations and pseudo-likelihood methods. They then briefly introduce conditional models and move on to the random-effects family, encompassing the beta-binomial model, the probit model and, in particular the generalized linear mixed model. Several frequently used procedures for model fitting are discussed and differences between marginal models and random-effects models are given attention.The authors consider a variety of extensions, such as models for multivariate longitudinal measurements, random-effects models with serial correlation, and mixed models with non-Gaussian random effects. They sketch the general principles for how to deal with the commonly encountered issue of incomplete longitudinal data.The authors critique frequently used methods and propose flexible and broadly valid methods instead, and conclude with key concepts of sensitivity analysis.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.

The book provides a comprehensive treatment of multidimensional scaling (MDS), a family of statistical techniques for analyzing the structure of (dis)similarity data. Such data are widespread, including, for example, intercorrelations of survey items, direct ratings on the similarity on choice objects, or trade indices for a set of countries. MDS represents the data as distances among points in a geometric space of low dimensionality. This map can help to see patterns in the data that are not obvious from the data matrices. MDS is also used as a psychological model for judgments of similarity and preference.This book may be used as an introduction to MDS for students in psychology, sociology, and marketing. The prerequisite is an elementary background in statistics. The book is also well suited for a variety of advanced courses on MDS topics. All the mathematics required for more advanced topics is developed systematically.This second edition is not only a complete overhaul of its predecessor, but also adds some 140 pages of new material. Many chapters are revised or have sections reflecting new insights and developments in MDS.There are two new chapters, one on asymmetric models and the other on unfolding. There are also numerous exercises that help the reader to practice what he or she has learned, and to delve deeper into the models and its intricacies. These exercises make it easier to use this edition in a course. All data sets used in the book can be downloaded from the web. The appendix on computer programs has also been updated and enlarged to reflect the state of the art.

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.

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.

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.

This volume is the first book-length treatment of model-based geostatistics. The text is expository, emphasizing statistical methods and applications rather than the underlying mathematical theory. It features analyses of datasets from a range of scientific contexts.

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 is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show 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, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

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.

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 recent 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.

Statisticians, probabilists, and mathematicians will all be interested in a expanded version of this classic work on inequalities. The theory of inequalities has applications in virtually every branch of mathematics.

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.

This book is intended for graduate students in statistics and industrial mathematics, as well as researchers and practitioners in the field. We cover both theory and practice of nonparametric estimation. The text is novel in its use of maximum penalized likelihood estimation, and the theory of convex minimization problems (fully developed in the text) to obtain convergence rates. We also use (and develop from an elementary view point) discrete parameter submartingales and exponential inequalities. A substantial effort has been made to discuss computational details, and to include simulation studies and analyses of some classical data sets using fully automatic (data driven) procedures. Some theoretical topics that appear in textbook form for the first time are definitive treatments of I.J. Good's roughness penalization, monotone and unimodal density estimation, asymptotic optimality of generalized cross validation for spline smoothing and analogous methods for ill-posed least squares problems, and convergence proofs of EM algorithms for random sampling problems.

Now available in paperback. Elements of Multivariate Time Series Analysis, Second Edition introduces the basic concepts and methods that are useful in the analysis and modeling of multivariate time series data that may arise in business and economics, engineering, geophysical sciences, and other fields. The book concentrates on the time-domain analysis of multivariate time series, and assumes a background in univariate time series analysis. It covers basic topics such as stationary processes and their covariance matrix structure, vector AR, MA, and ARMA models, forecasting, least squares and maximum likelihood estimation for ARMA models, associated likelihood ratio testing procedures, and other model specification methods useful for model building and model checking. In this revised edition, additional topics have been added and parts of the first edition have been expanded. The most notable addition is a new chapter that discusses topics that arise when exogenous variables are involved in model structures, generally through consideration of the ARMAX models. The book also includes exercise sets and multivariate time series data sets.In addition to serving as a textbook, this book will also be useful to researchers and graduate students in the areas of statistics, econometrics, business, and engineering.