Springer Texts in Statistics – serie

This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.

This 5th edition of this popular graduate textbook presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. It includes numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The R package ‘astsa’ has had major updates and the text will reflect those updates. In general, the graphics have been improved. New topics include random number generation, modeling and fitting predator-prey interactions, more emphasis on structural models, testing for linearity, discussion of EM algorithm is more extensive, Bayesian analysis of state space models and MCMC is more extensive (including new scripts in astsa), particle methods are introduced, stochastic volatility coverage is expanded, changepoint detection is introduced (new topic).The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, ARMAX models, stochastic volatility, and Markov chain Monte Carlo integration methods.This edition includes R code for each numerical example.

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance, marketing, and astrophysics in the past twenty years.

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform.Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.This Second Edition features new chapters on deep learning, survival analysis, and multiple testing, as well as expanded treatments of naïve Bayes, generalized linear models, Bayesian additive regression trees, and matrix completion. R code has been updated throughout to ensure compatibility.

Categorical data arise often in many fields, including biometrics, economics, management, manufacturing, marketing, psychology, and sociology. This book provides an introduction to the analysis of such data. The coverage is broad, using the loglinear Poisson regression model and logistic binomial regression models as the primary engines for methodology. Topics covered include count regression models, such as Poisson, negative binomial, zero-inflated, and zero-truncated models; loglinear models for two-dimensional and multidimensional contingency tables, including for square tables and tables with ordered categories; and regression models for two-category (binary) and multiple-category target variables, such as logistic and proportional odds models. All methods are illustrated with analyses of real data examples, many from recent subject area journal articles. These analyses are highlighted in the text, and are more detailed than is typical, providing discussion of the context and background of the problem, model checking, and scientific implications. More than 200 exercises are provided, many also based on recent subject area literature.Data sets and computer code are available at a web site devoted to the text. Adopters of this book may request a solutions manual from: textbook@springer-ny. com. Jeffrey S. Simonoff is Professor of Statistics at New York University. He is author of Smoothing Methods in Statistics and coauthor of A Casebook for a First Course in Statistics and Data Analysis, as well as numerous articles in scholarly journals. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute.

This book focuses on tools and techniques for building regression models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models. Plots are shown to be an important tool for both building regression models and assessing their validity. We shall see that deciding what to plot and how each plot should be interpreted will be a major challenge. In order to overcome this challenge we shall need to understand the mathematical properties of the fitted regression models and associated diagnostic procedures. As such this will be an area of focus throughout the book. In particular, we shall carefully study the properties of resi- als in order to understand when patterns in residual plots provide direct information about model misspecification and when they do not. The regression output and plots that appear throughout the book have been gen- ated using R. The output from R that appears in this book has been edited in minor ways. On the book web site you will find the R code used in each example in the text.

This textbook emphasizes the applications of statistics and probability to finance. Students are assumed to have had a prior course in statistics, but no background in finance or economics. The basics of probability and statistics are reviewed and more advanced topics in statistics, such as regression, ARMA and GARCH models, the bootstrap, and nonparametric regression using splines, are introduced as needed. The book covers the classical methods of finance such as portfolio theory, CAPM, and the Black-Scholes formula, and it introduces the somewhat newer area of behavioral finance. Applications and use of MATLAB and SAS software are stressed. The book will serve as a text in courses aimed at advanced undergraduates and masters students in statistics, engineering, and applied mathematics as well as quantitatively oriented MBA students. Those in the finance industry wishing to know more statistics could also use it for self-study.

Monte Carlo statistical methods, particularly those based on Markov chains, are now an essential component of the standard set of techniques used by statisticians. This new edition has been revised towards a coherent and flowing coverage of these simulation techniques, with incorporation of the most recent developments in the field. In particular, the introductory coverage of random variable generation has been totally revised, with many concepts being unified through a fundamental theorem of simulation There are five completely new chapters that cover Monte Carlo control, reversible jump, slice sampling, sequential Monte Carlo, and perfect sampling. There is a more in-depth coverage of Gibbs sampling, which is now contained in three consecutive chapters. The development of Gibbs sampling starts with slice sampling and its connection with the fundamental theorem of simulation, and builds up to two-stage Gibbs sampling and its theoretical properties. A third chapter covers the multi-stage Gibbs sampler and its variety of applications. Lastly, chapters from the previous edition have been revised towards easier access, with the examples getting more detailed coverage. This textbook is intended for a second year graduate course, but will also be useful to someone who either wants to apply simulation techniques for the resolution of practical problems or wishes to grasp the fundamental principles behind those methods. The authors do not assume familiarity with Monte Carlo techniques (such as random variable generation), with computer programming, or with any Markov chain theory (the necessary concepts are developed in Chapter 6). A solutions manual, which covers approximately 40% of the problems, is available for instructors who require the book for a course. Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at Université Paris Dauphine, France. He is also Head of the Statistics Laboratoryat the Center for Research in Economics and Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris, and Adjunct Professor at Ecole Polytechnique. He has written three other books and won the 2004 DeGroot Prize for The Bayesian Choice, Second Edition, Springer 2001. He also edited Discretization and MCMC Convergence Assessment, Springer 1998. He has served as associate editor for the Annals of Statistics, Statistical Science and the Journal of the American Statistical Association. He is a fellow of the Institute of Mathematical Statistics, and a winner of the Young Statistician Award of the Société de Statistique de Paris in 1995. George Casella is Distinguished Professor and Chair, Department of Statistics, University of Florida. He has served as the Theory and Methods Editor of the Journal of the American Statistical Association and Executive Editor of Statistical Science. He has authored three other textbooks: Statistical Inference, Second Edition, 2001, with Roger L. Berger; Theory of Point Estimation, 1998, with Erich Lehmann; and Variance Components, 1992, with Shayle R. Searle and Charles E. McCulloch. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association, and an elected fellow of the International Statistical Institute.

The goal of this text is to provide the reader with a single book where they can find a brief account of many, modern topics in nonparametric inference. The book is aimed at Master's level or Ph. D. level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. This text covers a wide range of topics including: the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book has a mixture of methods and theory.

This book arose out of two graduate courses that the authors have taught duringthepastseveralyears;the?rstonebeingonmeasuretheoryfollowed by the second one on advanced probability theory. The traditional approach to a ?rst course in measure theory, such as in Royden (1988), is to teach the Lebesgue measure on the real line, then the p di?erentation theorems of Lebesgue, L -spaces on R, and do general m- sure at the end of the course with one main application to the construction of product measures. This approach does have the pedagogic advantage of seeing one concrete case ?rst before going to the general one. But this also has the disadvantage in making many students’ perspective on m- sure theory somewhat narrow. It leads them to think only in terms of the Lebesgue measure on the real line and to believe that measure theory is intimately tied to the topology of the real line. As students of statistics, probability, physics, engineering, economics, and biology know very well, there are mass distributions that are typically nonuniform, and hence it is useful to gain a general perspective. This book attempts to provide that general perspective right from the beginning. The opening chapter gives an informal introduction to measure and integration theory. It shows that the notions of ?-algebra of sets and countable additivity of a set function are dictated by certain very na- ral approximation procedures from practical applications and that they are not just some abstract ideas.

This book is a contemporary introduction to theory, methods and computation in Bayesian Analysis. It focuses on topics that have stood the test of time and emerging areas such as reference priors, objective Bayes testing, Bayesian model selection and wavelets. No other such book is available in the market.

Longitudinal data are ubiquitous across Medicine, Public Health, Public Policy, Psychology, Political Science, Biology, Sociology and Education, yet many longitudinal data sets remain improperly analyzed. This book teaches the art and statistical science of modern longitudinal data analysis. The author emphasizes specifying, understanding, and interpreting longitudinal data models. He inspects the longitudinal data graphically, analyzes the time trend and covariates, models the covariance matrix, and then draws conclusions. Covariance models covered include random effects, autoregressive, autoregressive moving average, antedependence, factor analytic, and completely unstructured models among others. Longer expositions explore: an introduction to and critique of simple non-longitudinal analyses of longitudinal data, missing data concepts, diagnostics, and simultaneous modeling of two longitudinal variables. Applications and issues for random effects models cover estimation, shrinkage, clustered data, models for binary and count data and residuals and residual plots.Shorter sections include a general discussion of how computational algorithms work, handling transformed data, and basic design issues.This book requires a solid regression course as background and is particularly intended for the final year of a Biostatistics or Statistics Masters degree curriculum. The mathematical prerequisite is generally low, mainly assuming familiarity with regression analysis in matrix form. Doctoral students in Biostatistics or Statistics, applied researchers and quantitative doctoral students in disciplines such as Medicine, Public Health, Public Policy, Psychology, Political Science, Biology, Sociology and Education will find this book invaluable. The book has many figures and tables illustrating longitudinal data and numerous homework problems. The associated web site contains many longitudinal data sets, examples of computer code, and labs to re-enforce the material.

This book is for people who want to learn probability and statistics quickly. It brings together many of the main ideas in modern statistics in one place. The book is suitable for students and researchers in statistics, computer science, data mining and machine learning. This book covers a much wider range of topics than a typical introductory text on mathematical statistics. It includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses. The reader is assumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. The text can be used at the advanced undergraduate and graduate level.

Now available in paperback. This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated are independence, interchangeability,and martingales; particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familar with measure theory as indicated by the guidelines in the preface.Special features include: A comprehensive treatment of the law of the iterated logarithm; the Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof; development and applications of the second moment analogue of Wald's equation; limit theorems for martingale arrays, the central limit theorem for the interchangeable and martingale cases, moment convergence in the central limit theorem; complete discussion, including central limit theorem, of the random casting of r balls into n cells; recent martingale inequalities; Cram r-L vy theore and factor-closed families of distributions. This edition includes a section dealing with U-statistic, adds additional theorems and examples, and includes simpler versions of some proofs.

This graduate-level textbook, now in paperback, presents an introduction to Bayesian statistics and decision theory. Its scope covers both the basic ideas of statistical theory and some modern and advanced topics of Bayesian statistics.

Time Series Analysis With Applications in R, Second Edition, presents an accessible approach to understanding time series models and their applications. Although the emphasis is on time domain ARIMA models and their analysis, the new edition devotes two chapters to the frequency domain and three to time series regression models, models for heteroscedasticity, and threshold models. All of the ideas and methods are illustrated with both real and simulated data sets. A unique feature of this edition is its integration with the R computing environment. The tables and graphical displays are accompanied by the R commands used to produce them. An extensive R package, TSA, which contains many new or revised R functions and all of the data used in the book, accompanies the written text. Script files of R commands for each chapter are available for download. There is also an extensive appendix in the book that leads the reader through the use of R commands and the new R package to carry out the analyses.

Statistical design is one of the fundamentals of our subject, being at the core of the growth of statistics during the previous century. Design played a key role in agricultural statistics and set down principles of good practic, principles that still apply today. Statistical design is all about understanding where the variance comes from, and making sure that is where the replication is. Indeed, it is probably correct to say that these principles are even more important today.

This book developed out of my year-long course on asymptotic theory at Purdue University. Numeroustopics covered in this book are available in the literature in a scattered manner, and they are brought together under one umbrella in this book.

The authors here present statistical methods and models of importance to quantitative finance and links finance theory to market practice via statistical modeling and decision making. They provide basic statistical background as well as in-depth applications.

This book details developments that have led to the introduction of many innovative statistical tools for high-dimensional data analysis. It takes a broad perspective, covering both linear and nonlinear methods.

This undergraduate statistical quality assurance textbook clearly shows with real projects, cases and data sets how statistical quality control tools are used in practice.  Among the topics covered is a practical evaluation of measurement effectiveness for both continuous and discrete data.  Gauge Reproducibility and Repeatability methodology (including confidence intervals for Repeatability, Reproducibility and the Gauge Capability Ratio) is thoroughly developed. Process capability indices and corresponding confidence intervals are also explained.  In addition to process monitoring techniques, experimental design and analysis for process improvement are carefully presented. Factorial and Fractional Factorial arrangements of treatments and Response Surface methods are covered.Integrated throughout the book are rich sets of examples and problems that help readers gain a better understanding of where and how to apply statistical quality control tools.  These large and realistic problem sets in combination with the streamlined approach of the text and extensive supporting material facilitate reader understanding.Second Edition ImprovementsExtensive coverage of measurement quality evaluation (in addition to ANOVA Gauge R&R methodologies)New end-of-section exercises and revised-end-of-chapter exercisesTwo full sets of slides, one with audio to assist student preparation outside-of-class and another appropriate for professors’ lecturesSubstantial supporting materialSupporting MaterialSeven R programs that support variables and attributes control chart construction and analyses, Gauge R&R methods, analyses of Fractional Factorial studies,  Propagation of Error analyses and Response Surface analysesDocumentation for the R programsExcel data files associated with theend-of-chapter problem sets, most from real engineering settings

* A self-contained introduction to probability, exchangeability and Bayes' rule provides a theoretical understanding of the applied material. * Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. * The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential.The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis.The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix.

This is a textbook which will provide students with a straightforward introduction to the mathematical theory of probability. It is written with the aim of presenting the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Any graduate student who has a familiarity with real analysis will be able to use this text - measure theory is used only where necessary and undue abstraction is avoided. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text.

The last two decades have seen structural equation modeling (SEM) emerge as a powerful data analysis tool for research in the social sciences, education, and psychology. With the advent of SEM computer programs such as LISREL and EQS, SEM has become a well-established and respected methodology. This book provides an introduction to the subject suitable for beginning graduate students. Its focus is on the basic concepts and applications of SEM within the social and behavioral sciences. The author develops SEM techniques by presenting linear regression, path analysis, confirmatory factor analysis, and then more general structural equation models. In doing so, he is able both to explain clearly the underlying statistical methodology in SEM whilst at the same time illustrate the use of SEM to analyse real data sets drawn from a number of different settings in the behavioral and social sciences.

This textbook is ideal for an undergraduate introduction to probability, with a calculus prerequisite. It is based on a course that the author has taught many times at Berkeley. The text's overall style is informal, but all results are stated precisely, and most are proved. Understanding is developed through intuitive explanations and examples. Graphs, diagrams, and geometrical ideals motivate results that might otherwise look likely purely formal manipulations.

Graphic modelling is a form of multivariate analysis that uses graphs to represent models. These graphs display the structure of dependencies, both associational and causal, between the variables in the model. This textbook provides an introduction to graphical modelling with emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, a freeware version of which can be downloaded from the Internet. Following an introductory chapter which sets the scene and describes some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to the second edition. Chapter 7 describes the use of directed graphs, chain graphs, and other graphs. Chapter 8 summarizes some recent work on causal inference, relevant when graphical models are given a causal interpretation. This book will provide a useful introduction to this topic for students and researchers.

This book describes the basis, application, and interpretation of statistics, and presents a wide range of univariate and multivariate statistical methodology. In its first edition it has proved popular across all science and technology based disciplines, including the social sciences, and in areas of commerce. It is used both as a reference on statistical methodology for researchers and technicians, and as a textbook with particular appeal for graduate classes containing students of mixed mathematical and statistical background. The book is developed without the use of calculus, although several self-contained sections containing calculus are included to provide additional insight for readers who have a calculus background. Based on the author's "Statistics in Scientific Investigation," the book has been extended substantially in the area of multivariate applications and through the expansion of logistic regression and log linear methodology. It presumes readers have access to a statistical computing package and includes guidance on the application of statistical computing packages.The new edition retains the unique feature of being written from the users' perspective; it connects statistical models and methods to investigative questions and background information, and connects statistical results with interpretations in plain English. In keeping with this approach, methods are grouped by usage rather than by commonality of statistical methodology. Guidance is provided on the choice of appropriate methods. The use of real life examples has been retained and expanded. Using the power of the Internet, expanded reports on the examples are available at a Springer Web site as Word documents. Additionaly, all data sets are available at the Web site as Excel files, and program files and data sets are provided for SAS users and SPSS users. The programs are annotated so users can adapt.

Winner of the 2004 DeGroot PrizeThe DeGroot Prize is awarded every two years by the International Societyfor Bayesian Analysis in recognition of an important, timely, thorough andnotably original contribution to the statistics literature.This graduate-level textbook presents an introduction to Bayesian statistics and decision theory. Its scope covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, the Stein effect, Bayesian model choice, hierarchical and empirical Bayes modeling, Monte Carlo integration, including Gibbs sampling and other MCMC techniques. The second edition includes a new chapter on model choice (Chapter 7) and the chapter on Bayesian calculations (6) has been extensively revised. Chapter 4 includes a new section on dynamic models. In Chapter 3, the material on noninformative priors has been expanded, and Chapter 10 has been supplemented with more examples. The Bayesian Choice will be suitable as a text for courses on Bayesian analysis, decision theory or a combination of them. Christian P.Robert is Professor of Statistics in the Applied Mathematics Department at the Universite Paris Dauphine, and external lecturer at Ecole Polytechnique, Palaiseau, France. He was previously Head of the Statistics Laboratory at the Center for Research in Economics and Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris. In addition to many papers on Bayesian statistics, simulation methods, and decision theory, he has written three other books, including Monte Carlo Statistical Method (Springer 1999) with George Casella. He also edited Discretization and MCMC Convergence Assessment (Springer 1998). He has served or is serving as an associate editor for the Annals of Statistics, the Journal of the American Statistical Association, Statistical Science, and Sankhya. He is a fellow of the Institute of Mathematical Statistics, and the Young Statistician Award of the Societe de Statistique de Paris in 1995.