Unique blend of asymptotic theory and small sample practice through simulation experiments and data analysis.

Novel reproducing kernel Hilbert space methods for the analysis of smoothing splines and local polynomials. Leading to uniform error bounds and honest confidence bands for the mean function using smoothing splines

Exhaustive exposition of algorithms, including the Kalman filter, for the computation of smoothing splines of arbitrary order.

This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each chapter for their well prepared manuscripts and the stimulating conferences they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book."

This volume gathers selected peer-reviewed papers presented at the international conference "MAF 2016 - Mathematical and Statistical Methods for Actuarial Sciences and Finance", held in Paris (France) at the Universite Paris-Dauphine from March 30 to April 1, 2016. The contributions highlight new ideas on mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field, one that yields unique theoretical models and practical applications, as well as new insights in the discussion of problems of national and international interest. This volume is addressed to academicians, researchers, Ph.D. students and professionals.

1. 1 Introduction This book is written in four major divisions. The first part is the introductory chapters consisting of Chapters 1 and 2. In part two, Chapters 3-11, we develop fuzzy estimation. For example, in Chapter 3 we construct a fuzzy estimator for the mean of a normal distribution assuming the variance is known. More details on fuzzy estimation are in Chapter 3 and then after Chapter 3, Chapters 4-11 can be read independently. Part three, Chapters 12- 20, are on fuzzy hypothesis testing. For example, in Chapter 12 we consider the test Ho : /1 = /10 verses HI : /1 f=- /10 where /1 is the mean of a normal distribution with known variance, but we use a fuzzy number (from Chapter 3) estimator of /1 in the test statistic. More details on fuzzy hypothesis testing are in Chapter 12 and then after Chapter 12 Chapters 13-20 may be read independently. Part four, Chapters 21-27, are on fuzzy regression and fuzzy prediction. We start with fuzzy correlation in Chapter 21. Simple linear regression is the topic in Chapters 22-24 and Chapters 25-27 concentrate on multiple linear regression. Part two (fuzzy estimation) is used in Chapters 22 and 25; and part 3 (fuzzy hypothesis testing) is employed in Chapters 24 and 27. Fuzzy prediction is contained in Chapters 23 and 26. A most important part of our models in fuzzy statistics is that we always start with a random sample producing crisp (non-fuzzy) data.

This book covers all types of literature on existing trend analysis approaches, but more than 60% of the methodologies are developed here and some of them are reflected to scientific literature and others are also innovative versions, modifications or improvements. The suggested methodologies help to design, develop, manage and deliver scientific applications and training to meet the needs of interested staff in companies, industries and universities including students. Technical content and expertise are also provided from different theoretical and especially active roles in the design, development and delivery of science in particular and economics and business in general. It is also ensured that, wherever possible and technically appropriate, priority is given to the inclusion and integration of real life data, examples and processes within the book content. The time seems right, because available books just focus on special sectors (fashion, social, business). This book reviews all the available trend approaches in the present literature on rational and logical bases.

The Palm theory and the Loynes theory of stationary systems are the two pillars of the modern approach to queuing. This book, presenting the mathematical foundations of the theory of stationaryqueuing systems, contains a thorough treatment of both of these.

This approach helps to clarify the picture, in that it separates the task of obtaining the key system formulas from that of proving convergence to a stationary state and computing its law.

The theory is constantly illustrated by classical results and models: Pollaczek-Khintchin and Tacacs formulas, Jackson and Gordon-Newell networks, multiserver queues, blocking queues, loss systems etc., but it also contains recent and significant examples, where the tools developed turn out to be indispensable.

Several other mathematical tools which are useful within this approach are also presented, such as the martingale calculus for point processes, or stochastic ordering for stationary recurrences.

This thoroughly revised second edition contains substantial additions - in particular, exercises and their solutions - rendering this now classic reference suitable for use as a textbook.

This volume highlights Prof. Hira Koul's achievements in many areas of Statistics, including Asymptotic theory of statistical inference, Robustness, Weighted empirical processes and their applications, Survival Analysis, Nonlinear time series and Econometrics, among others. Chapters are all original papers that explore the frontiers of these areas and will assist researchers and graduate students working in Statistics, Econometrics and related areas. Prof. Hira Koul was the first Ph.D. student of Prof. Peter Bickel. His distinguished career in Statistics includes the receipt of many prestigious awards, including the Senior Humbolt award (1995), and dedicated service to the profession through editorial work for journals and through leadership roles in professional societies, notably as the past president of the International Indian Statistical Association. Prof. Hira Koul has graduated close to 30 Ph.D. students, and made several seminal contributions in about 125 innovative research papers. The long list of his distinguished collaborators is represented by the contributors to this volume.

Scientists today 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 modelling, 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 drwan from growth analysis, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology 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. Much of the material is based on the authors' own work, some of which appears here for the first time. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He draws on his collaboration with researchers in speech articulation, motor control, meteorology, psychology, and human physiology to illustrate his technical contributions to functional data analysis in a wide range of statistical and application journals. Bernard Silverman, author of the highly regarded "Density Estimation for Statistics and DataAnalysis," and coauthor of "Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach," is Professor of Statistics at Bristol University. His published work on smoothing methods and other aspects of applied, computational, and theoretical statistics has been recognized by the Presidents' Award of the Committee of Presidents of Statistical Societies, and the award of two Guy Medals by the Royal Statistical Society.

Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled with instabilities, can result in highly irregular behavior. This book gives a unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, a general finite dimensional theory of homoclinic jumping is developed and illustrated with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context. Previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds are described. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics. The theory is further used to study resonances in Hamiltonian systems with applications to molecular dynamics and rigid body motion. The final chapter contains an infinite dimensional extension of the finite dimensional theory, with application to the perturbed nonlinear Schrodinger equation and coupled NLS equations."

This book provides the readers with the overall latest research on think tanks, summarizing the characteristics of think tanks, revealing the general laws and internal logic of think tank research, applying systems, dialectical views and operations research, system theory, and cybernetics to the problems existing in the research work of think tanks at home and abroad. Based on problem-oriented, evidence-oriented and scientific orientation, this book systematically considers the methodology of think tank research, proposes the DIIS theoretical method system of think tank research, defines the standardization process of think tank research and the quality standard of think tank DIIS, and gives corresponding DIIS to the actual think tank research problem. The method aims to improve the scientificity, effectiveness, and reliability of the research results of think tanks, provide systematic theoretical analysis for think tank research, promote the professional development of think tanks, and better serve the modernization of national governance systems and governance capabilities. This book presents new theoretical and research method support and reference that contribute to macro decision-making departments, management departments, scientific research institutes, universities, and enterprises think tank research related departments, strategic decision makers, think tank managers, think tank researchers, and readers interested in think tanks reading and using. Finally yet importantly, this book embodies the research of think tank as the object of investigation, jumping out of specific social conditions, using systemic thoughts, thinking about the more general role and characteristics of think tanks from the theoretical level, important theoretical issues such as principles and logic systems that think tank research should follow.

The intersection of probability and physics has been a rich and explosive area of growth in the past two decades, specifically covering such subjects as percolation theory, random walks, interacting particle systems, and various topics related to statistical mechanics. In the last several years, substantial progress has been made in a number of directions: fluctuations of 2-dimensional growth processes, Wulf constructions in higher dimensions for percolation, Potts and Ising models, classification of random walks in random environments, the introduction of the stochastic Loewner equation, the rigorous proof of intersection exponents for planar Brownian motion, and finally the proof of conformal invariance for critical percolation on the triangular lattice. This volume consists of a collection of invited articles, written by some of the most distinguished probabilists in the above-mentioned areas, most of whom were personally responsible for advances in the various subfields of probability. All of the articles are an outgrowth of the Fourth Brazilian School of Probability, held in Mambucaba, Brazil, August 2000. Contributors: K. Alexander * J.M. AzaAs * J. van den Berg * T. Bodineau * F. Camia * N. Cancrini * G. Grimmett * P. Hiemer * A.E. Holroyd * H. Kesten * G.F. Lawler * T.M. Liggett * J. Lorinczi * F. Martinelli * C. M. Newman * J. Quastel * C.-E. Pfister * M. PrAhofer * C. Roberto * O. Schramm * V. Sidoravicius * H. Spohn * A. Toom * B. TA3th * D. Ueltschi * W. Werner * M. Wschebor * M. WA1/4thrich Graduate students and researchers in probability theory and math physics will find this book a useful reference.

This volume begins with a description of Alladi Ramakrishnan's remarkable scientific career and his grand vision that led to the creation of The Institute of Mathematical Sciences (MATSCIENCE), in Madras (now Chennai), India, in 1962. The lists of his research publications, his PhD students, and other relevant facts relating to his eventful career are included. The inclusion of both research and survey articles by leading mathematicians, statisticians, and physicists who got to know Alladi Ramakrishnan over the years and admired his significant contributions to research and to the scientific profession, have been written and dedicated in this volume to Ramakrishnan's memory.

Developed from the Second International Congress on Actuarial Science and Quantitative Finance, this volume showcases the latest progress in all theoretical and empirical aspects of actuarial science and quantitative finance. Held at the Universidad de Cartagena in Cartegena, Colombia in June 2016, the conference emphasized relations between industry and academia and provided a platform for practitioners to discuss problems arising from the financial and insurance industries in the Andean and Caribbean regions. Based on invited lectures as well as carefully selected papers, these proceedings address topics such as statistical techniques in finance and actuarial science, portfolio management, risk theory, derivative valuation and economics of insurance.

The 1952 Nobel physics laureate Felix Bloch (1905-83) was one of the titans of twentieth-century physics. He laid the fundamentals for the theory of solids and has been called the "father of solid-state physics." His numerous, valuable contributions include the theory of magnetism, measurement of the magnetic moment of the neutron, nuclear magnetic resonance, and the infrared problem in quantum electrodynamics.Statistical mechanics is a crucial subject which explores the understanding of the physical behaviour of many-body systems that create the world around us. Bloch's first-year graduate course at Stanford University was the highlight for several generations of students. Upon his retirement, he worked on a book based on the course. Unfortunately, at the time of his death, the writing was incomplete.This book has been prepared by Professor John Dirk Walecka from Bloch's unfinished masterpiece. It also includes three sets of Bloch's handwritten lecture notes (dating from 1949, 1969 and 1976), and details of lecture notes taken in 1976 by Brian Serot, who gave an invaluable opinion of the course from a student's perspective. All of Bloch's problem sets, some dating back to 1933, have been included.The book is accessible to anyone in the physical sciences at the advanced undergraduate level or the first-year graduate level.

This book contains a collection of original and state-of-the-art contributions in rational choice and general equilibrium theory. Among the topics are preferences, demand, equilibrium, core allocations, and testable restrictions. The contributing authors are Daniel McFadden, Rosa Matzkin, Emma Moreno-Garcia, Roger Lagunoff, Yakar Kannai, Myrna Wooders, James Moore, Ted Bergstrom, Luca Anderlini, Lin Zhou, Mark Bagnoli, Alexander Kovalenkov, Carlos Herves-Beloso, Michaela Topuzu, Bernard Cornet, Andreu Mas-Colell and Nicholas Yannelis.

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference Fourier Analysis and Pseudo-Differential Operators, June 25 30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series Fourier Analysis and Partial Differential Equations. "

After the ?rst edition of this book was published in early 2005, the world has changed dramatically and at a pace never seen before. The changes that - curred in 2008 and 2009 were completely unthinkable two years before. These changes took place not only in the Finance sector, the origin of the crisis, but also, as a result, in other economic sectors like the automotive sector. Governments now own substantial parts, if not majorities, in banks or other companies which recorded losses of double digit billions of USD in 2008. 2008 saw the collapse of leading stand-alone U. S. investment banks. In many co- tries interest rates fell close to zero. What has happend? While the economy showed strong growth in 2004 to 2006, the Subprime or Credit Crisis changed the picture completely. What started in the U. S. ho- ing market in late 2006 became a full-?edged global ?nancial crisis and has a?ected ?nancial markets around the world. A decline in U. S. house prices and increasing interest rates caused a higher rate of subprime mortgage delinqu- cies in the U. S. and, due to the wide distribution of securitized assets, had a negative e?ect on other markets. As a result, markets realized that risks had been underestimated and volatility increased. This development culminated in the bankruptcy of the investment bank Lehman Brothers in mid September 2008.

Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines.

With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms available in a single resource. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Bridging the gap between statistical theory and physical experiment, this is a thorough introduction to the statistical methods used in the experimental physical sciences and to the numerical methods used to implement them. An accompanying CD-ROM provides detailed code for implementing many of these algorithms. The treatment emphasises concise but rigorous mathematics but always retains its focus on applications. Readers are assumed to have a sound basic knowledge of differential and integral calculus and some knowledge of vectors and matrices. After an introduction to probability, random variables, computer generation of random numbers and important distributions, the book turns to statistical samples, the maximum likelihood method, and the testing of statistical hypotheses. The discussion concludes with several important statistical methods: least squares, analysis of variance, polynomial regression, and analysis of time series. Appendices provide the necessary methods of matrix algebra, combinatorics, and many sets of useful algorithms and formulae.

This book collects important advances in methodology and data analysis for directional statistics. It is the companion book of the more theoretical treatment presented in Modern Directional Statistics (CRC Press, 2017). The field of directional statistics has received a lot of attention due to demands from disciplines such as life sciences or machine learning, the availability of massive data sets requiring adapted statistical techniques, and technological advances. This book covers important progress in bioinformatics, biology, astrophysics, oceanography, environmental sciences, earth sciences, machine learning and social sciences.

This contributed volume contains fourteen papers based on selected presentations from the European Conference on Game Theory SING11-GTM 2015, held at Saint Petersburg State University in July 2015, and the Networking Games and Management workshop, held at the Karelian Research Centre of the Russian Academy of Sciences in Petrozvavodsk, Russia, also in July 2015. These papers cover a wide range of topics in game theory, including recent advances in areas with high potential for future work, as well as new developments on classical results. Some of these include A new approach to journal ranking using methods from social choice theory; A differential game of a duopoly in which two firms are competing for market share in an industry with network externalities; The impact of information propagation in the model of tax audits; A voting model in which the results of previous votes can affect the process of coalition formation in a decision-making body; The Selten-Szidarovsky technique for the analysis of Nash equilibria of games with an aggregative structure; Generalized nucleoli and generalized bargaining sets for games with restricted cooperation; Bayesian networks and games of deterrence; and A new look at the study of solutions for games in partition function form. The maturity and vitality of modern-day game theory are reflected in the new ideas, novel applications, and contributions of young researchers represented in this collection. It will be of interest to anyone doing theoretical research in game theory or working on one its numerous applications.

This book provides a unique insight into the latest breakthroughs in a consistent manner, at a level accessible to undergraduates, yet with enough attention to the theory and computation to satisfy the professional researcher Statistical physics addresses the study and understanding of systems with many degrees of freedom. As such it has a rich and varied history, with applications to thermodynamics, magnetic phase transitions, and order/disorder transformations, to name just a few. However, the tools of statistical physics can be profitably used to investigate any system with a large number of components. Thus, recent years have seen these methods applied in many unexpected directions, three of which are the main focus of this volume. These applications have been remarkably successful and have enriched the financial, biological, and engineering literature. Although reported in the physics literature, the results tend to be scattered and the underlying unity of the field overlooked.

This book describes the development of what we would now regard as a class of statistical fitting procedures between 1750 and 1900. The book contains detailed algebraic descriptions of the fitting of linear relationships by the method of least squares and the closely related least absolute deviations and minimax absolute deviations procedures. The prerequisite is a basic course in mathematical statistics. The primary audience for this book will be statisticians concerned with the fitting of linear models. However, it will also be of interest to engineers and scientists concerned with the empirical determination of linear relationships.