This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.

Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal articles have described the reasons standard techniques can be unsatisfactory, but simple, intuitive explanations are generally unavailable. Situations arise where even highly nonsignificant results become significant when analyzed with more modern methods.

Without assuming the reader has any prior training in statistics, Part I of this book describes basic statistical principles from a point of view that makes their shortcomings intuitive and easy to understand. The emphasis is on verbal and graphical descriptions of concepts. Part II describes modern methods that address the problems covered in Part I. Using data from actual studies, many examples are included to illustrate the practical problems with conventional procedures and how more modern methods can make a substantial difference in the conclusions reached in many areas of statistical research.

The second edition of this book includes a number of advances and insights that have occurred since the first edition appeared. Included are new results relevant to medians, regression, measures of association, strategies for comparing dependent groups, methods for dealing with heteroscedasticity, and measures of effect size.

This book brings together aspects of statistics and machine learning to provide a comprehensive guide to evaluating, interpreting and understanding biometric data. It naturally leads to topics including data mining and prediction to be examined in detail. The book places an emphasis on the various performance measures available for biometric systems, what they mean, and when they should and should not be applied. The evaluation techniques are presented rigorously, however they are always accompanied by intuitive explanations. This is important for the increased acceptance of biometrics among non-technical decision makers, and ultimately the general public.

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis and related fields.

Specific topics covered include:

* non-parametric estimation of lifetimes of subjects exposed to radiation

* statistical analysis of simultaneous degradation-mortality data with covariates of the aged

* estimation of maintenance efficiency in semiparametric imperfect repair models

* cancer prognosis using survival forests

* short-term health problems related to air pollution: analysis using semiparametric generalized additive models

* parametric models in accelerated life testing and fuzzy data

* semiparametric models in the studies of aging and longevity

This book will be of use as a reference text for general statisticians, theoreticians, graduate students, reliability engineers, health researchers, and biostatisticians working in applied probability and statistics.

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike traditional deterministic algorithms, SD combines sampling approaches from the statistical literature with traditional mathematical programming constructs (e.g. decomposition, cutting planes etc.). This marriage of two highly computationally oriented disciplines leads to a line of work that is most definitely driven by computational considerations. Furthermore, the use of sampled data in SD makes it extremely flexible in its ability to accommodate various representations of uncertainty, including situations in which outcomes/scenarios can only be generated by an algorithm/simulation. The authors report computational results with some of the largest stochastic programs arising in applications. These results (mathematical as well as computational) are the tip of the iceberg'. Further research will uncover extensions of SD to a wider class of problems. Audience: Researchers in mathematical optimization, including those working in telecommunications, electric power generation, transportation planning, airlines and production systems. Also suitable as a text for an advanced course in stochastic optimization.

The fascinating correspondence between Paul Levy and Maurice Frechet spans an extremely active period in French mathematics during the twentieth century. The letters of these two Frenchmen show their vicissitudes of research and passionate enthusiasm for the emerging field of modern probability theory. The letters cover various topics of mathematical importance including academic careers and professional travels, issues concerning students and committees, and the difficulties both mathematicians met to be elected to the Paris Academy of Sciences. The technical questions that occupied Levy and Frechet on almost a daily basis are the primary focus of these letters, which are charged with elation, frustration and humour. Their mathematical victories and setbacks unfolded against the dramatic backdrop of the two World Wars and the occupation of France, during which Levy was obliged to go into hiding. The clear and persistent desire of these mathematicians to continue their work whatever the circumstance testifies to the enlightened spirit of their discipline which was persistent against all odds. The book contains a detailed and comprehensive introduction to the central topics of the correspondence. The original text of the letters is also annotated by numerous footnotes for helpful guidance. Paul Levy and Maurice Frechet will be useful to anybody interested in the history of mathematics in the twentieth century and, in particular, the birth of modern probab ility theory.

The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of them have applications in view, and some of them contain extensive illustrations of the applied techniques. This book will provide research workers and graduate students with a cross-section of innovative work in the fields of matrix methods and multivariate statistical analysis. It should be of interest to students and practitioners in a wide range of subjects which rely upon modern methods of statistical analysis. The contributors to the book are themselves practitioners of a wide range of subjects including econometrics, psychometrics, educational statistics, computation methods and electrical engineering, but they find a common ground in the methods which are represented in the book. It is envisaged that the book will serve as an important work of reference and as a source of inspiration for some years to come.

Richard De Veaux, Paul Velleman, and David Bock wrote Intro Stats with the goal that you have as much fun reading it as they did in writing it. Maintaining a conversational, humorous, and informal writing style, this new edition engages readers from the first page. The authors focus on statistical thinking throughout the text and rely on technology for calculations. As a result, students can focus on developing their conceptual understanding. Innovative Think/Show/Tell examples provide a problem-solving framework and, more importantly, a way to think through any statistics problem and present their results. New to the Fourth Edition is a streamlined presentation that keeps students focused on what's most important, while including out helpful features. An updated organization divides chapters into sections, with specific learning objectives to keep students on track. A detailed table of contents assists with navigation through this new layout. Single-concept exercises complement the existing mid- to hard-level exercises for basic skill development.

The subject of multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This introductory text provides students and researchers in the above fields with various ways of handling some of the useful but difficult concepts encountered in dealing with the machinery of multivariable analysis and differential forms on manifolds. The approach here is to make such concepts as concrete as possible.

Highlights and key features:

* systematic exposition, supported by numerous examples and exercises from the computational to the theoretical

* brief development of linear algebra in Rn

* review of the elements of metric space theory

* treatment of standard multivariable material: differentials as linear transformations, the inverse and implicit function theorems, Taylor's theorem, the change of variables for multiple integrals (the most complex proof in the book)

* Lebesgue integration introduced in concrete way rather than via measure theory

* latar chapters move beyond Rn to manifolds and analysis on manifolds, covering the wedge product, differential forms, and the generalized Stokes' theorem

* bibliography and comprehensive index

Core topics in multivariable analysis that are basic for senior undergraduates and graduate studies in differential geometry and for analysis in N dimensions and on manifolds are covered. Aside from mathematical maturity, prerequisites are a one-semester undergraduate course in advanced calculus or analysis, and linear algebra. Additionally, researchers working in the areas of dynamical systems, control theory and optimization, general relativity and electromagnetic phenomena may use the book as a self-study resource.

This text is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behaviour.

Space is increasingly recognized as a legitimate factor that influences many processes and conceptual frameworks, including notions of spatial coherence and spatial heterogeneity that have been demonstrated to provide substance to both theory and explanation. The potential and relevance of spatial analysis is increasingly understood by an expanding sphere of cogent disciplines that have adopted the tools of spatial analysis. This book brings together major new developments in spatial analysis techniques, including spatial statistics, econometrics, and spatial visualization, and applications to fields such as regional studies, transportation and land use, political and economic geography, population and health. Establishing connections to existing and emerging lines of research, the book also serves as a survey of the field of spatial analysis and its links with related areas.

Proceedings of the 5th Pannonian Symposium, Visegrad, Hungary, May 20-24, 1985

This volume deals with the analysis of nonlinear evolution problems described by partial differential equations having random or stochastic parameters. The emphasis throughout is on the actual determination of solutions, rather than on proving the existence of solutions, although mathematical proofs are given when this is necessary from an applications point of view. The content is divided into six chapters. Chapter 1 gives a general presentation of mathematical models in continuum mechanics and a description of the way in which problems are formulated. Chapter 2 deals with the problem of the evolution of an unconstrained system having random space-dependent initial conditions, but which is governed by a deterministic evolution equation. Chapter 3 deals with the initial-boundary value problem for equations with random initial and boundary conditions as well as with random parameters where the randomness is modelled by stochastic separable processes. Chapter 4 is devoted to the initial-boundary value problem for models with additional noise, which obey Ito-type partial differential equations. Chapter 5 is essential devoted to the qualitative and quantitative analysis of the chaotic behaviour of systems in continuum physics. Chapter 6 provides indications on the solution of ill-posed and inverse problems of stochastic type and suggests guidelines for future research. The volume concludes with an Appendix which gives a brief presentation of the theory of stochastic processes. Examples, applications and case studies are given throughout the book and range from those involving simple stochasticity to stochastic illposed problems. For applied mathematicians, engineers and physicists whosework involves solving stochastic problems.

This volume is a continuation of Unbiased Estimators and Their Applications, Vol. I: Univariate Case. It contains problems of parametric point estimation for multivariate probability distributions emphasizing problems of unbiased estimation. The volume consists of four chapters dealing, respectively, with some basic properties of multivariate continuous and discrete distributions, the general theory of point estimation in multivariate case, techniques for constructing unbiased estimators and applications of unbiased estimation theory in the multivariate case. These chapters contain numerous examples, many applications and are followed by a comprehensive Appendix which classifies and lists, in the form of tables, all known results relating to unbiased estimators of parameter functions for multivariate distributions. Audience: This volume will serve as a handbook on point unbiased estimation for researchers whose work involves statistics. It can also be recommended as a supplementary text for undergraduate and graduate students.

Masatoshi Fukushima is one of the most influential probabilists of our times. His fundamental work on Dirichlet forms and Markov processes made Hilbert space methods a tool in stochastic analysis and by this he opened the way to several new developments. His impact on a new generation of probabilists can hardly be overstated. These Selecta collect 25 of Fukushima's seminal articles published between 1967 and 2007.

The management of operational risk in the banking industry has undergone explosive changes over the last decade due to substantial changes in the operational environment. Globalization, deregulation, the use of complex financial products, and changes in information technology have resulted in exposure to new risks which are very different from market and credit risks. In response, the Basel Committee on Banking Supervision has developed a new regulatory framework for capital measurement and standards for the banking sector. This has formally defined operational risk and introduced corresponding capital requirements.

Many banks are undertaking quantitative modelling of operational risk using the Loss Distribution Approach (LDA) based on statistical quantification of the frequency and severity of operational risk losses. There are a number of unresolved methodological challenges in the LDA implementation. Overall, the area of quantitative operational risk is very new and different methods are under hot debate.

This book is devoted to quantitative issues in LDA. In particular, the use of Bayesian inference is the main focus. Though it is very new in this area, the Bayesian approach is well suited for modelling operational risk, as it allows for a consistent and convenient statistical framework for quantifying the uncertainties involved. It also allows for the combination of expert opinion with historical internal and external data in estimation procedures. These are critical, especially for low-frequency/high-impact operational risks.

This book is aimed at practitioners in risk management, academic researchers in financial mathematics, banking industry regulators and advanced graduate students in the area. It is a must-read for anyone who works, teaches or does research in the area of financial risk.

This book contains 12 contributions on stochastic models in reliability and maintenance. Written by the leading researchers on each topic, each contribution surveys the current status on stochastic models emphasizing mathematical formulation and optimization applications. Each contribution is self-contained and has a thorough bibliography. The topics include renewal processes, semi-Markov processes, Markovian deterioration models, maintenance and replacement models, software reliability models and Monte-Carlo simulation. This book provides researchers, reliability engineers and graduate students with the current status of the field and future developments of the subject.

Exploring Probability in School provides a new perspective into research on the teaching and learning of probability. It creates this perspective by recognizing and analysing the special challenges faced by teachers and learners in contemporary classrooms where probability has recently become a mainstream part of the curriculum from early childhood through high school. The authors of the book discuss the nature of probability, look at the meaning of probabilistic literacy, and examine student access to powerful ideas in probability during the elementary, middle, and high school years. Moreover, they assemble and analyse research-based pedagogical knowledge for teachers that can enhance the learning of probability throughout these school years.

With the booka (TM)s rich application of probability research to classroom practice, it will not only be essential reading for researchers and graduate students involved in probability education; it will also capture the interest of educational policy makers, curriculum personnel, teacher educators, and teachers.

Following the recent financial crisis, risk management in financial institutions, particularly in banks, has attracted widespread attention and discussion. Novel modeling approaches and courses to educate future professionals in industry, government, and academia are of timely relevance. This book introduces an innovative concept and methodology developed by the authors: active risk management. It is suitable for graduate students in mathematical finance/financial engineering, economics, and statistics as well as for practitioners in the fields of finance and insurance. The book s website features the data sets used in the examples along with various exercises."

Enrique Castillo is a leading figure in several mathematical and engineering fields. Organized to honor Castillo 's significant contributions, this volume is an outgrowth of the "International Conference on Mathematical and Statistical Modeling," and covers recent advances in the field. Applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented.

One service mathematics has rendered the 'Et BIOi. .... si j'avait su comment en revenir. human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Math@matics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

This volume dedicated to William Q. Meeker on the occasion of his sixtieth birthday is a collection of invited chapters covering recent advances in accelerated life testing and degradation models. The book covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics and finance. Additional topics covered include accelerated testing and inference, step-stress testing and inference, nonparametric inference, model validity in accelerated testing, the point process approach, bootstrap methods in degradation analysis, exact inferential methods in reliability, dynamic perturbed systems, and degradation models in statistics. Advances in Degradation Modeling is an excellent reference for researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance.

"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate: -Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans) -Various multi-target and multi-sensor tracking applications, -Practical applications in areas like distributed sensing and detection, -Related finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processes, Perfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.

Do you ever feel at a loss on how to proceed with a particular set of data? Your Statistical Consultant can provide the answer. This comprehensive guide introduces, describes, and makes recommendations regarding difficult statistical problems and techniques. The authors discuss common problems by addressing frequently asked questions; provide a conceptual overview of topics and techniques; give accounts of such new-found topics as the debate over statistical significance, effect sizes and meta-analysis; and highlight and explain key terms and points.

We present here a selection of the seminars given at the Second International Workshop on Instabilities and Nonequilibrium Structures in Valparaiso, Chile, in December 1987. The Workshop was organized by Facultad de Ciencias Fisicas y Matematicas of Universidad de Chile and by Universidad Tecnica Federico Santa Maria where it took place. This periodic meeting takes place every two years in Chile and aims to contribute to the efforts of Latin America towards the development of scientific research. This development is certainly a necessary condition for progress in our countries and we thank our lecturers for their warm collaboration to fulfill this need. We are also very much indebted to the Chilean Academy of Sciences for sponsoring officially this Workshop. We thank also our sponsors and supporters for their valuable help, and most especially the Scientific Cooperation Program of France, UNESCO, Ministerio de Educaci6n of Chile and Fundaci6n Andes. We are grateful to Professor Michiel Hazewinkel for including this book in his series and to Dr. David Larner of Kluwer for his continuous interest and support to this project.