This book presents a new branch of mathematical statistics aimed at constructing unimprovable methods of multivariate analysis, multi-parametric estimation, and discriminant and regression analysis. In contrast to the traditional consistent Fisher method of statistics, the essentially multivariate technique is based on the decision function approach by A. Wald. Developing this new method for high dimensions, comparable in magnitude with sample size, provides stable approximately unimprovable procedures in some wide classes, depending on an arbitrary function. A remarkable fact is established: for high-dimensional problems, under some weak restrictions on the variable dependence, the standard quality functions of regularized multivariate procedures prove to be independent of distributions. For the first time in the history of statistics, this opens the possibility to construct unimprovable procedures free from distributions. Audience: This work will be of interest to researchers and graduate students whose work involves statistics and probability, reliability and risk analysis, econometrics, machine learning, medical statistics, and various applications of multivariate analysis.

Data mining is the process of extracting hidden patterns from data, and it's commonly used in business, bioinformatics, counter-terrorism, and, increasingly, in professional sports. First popularized in Michael Lewis' best-selling Moneyball: The Art of Winning An Unfair Game, it is has become an intrinsic part of all professional sports the world over, from baseball to cricket to soccer. While an industry has developed based on statistical analysis services for any given sport, or even for betting behavior analysis on these sports, no research-level book has considered the subject in any detail until now. Sports Data Mining brings together in one place the state of the art as it concerns an international array of sports: baseball, football, basketball, soccer, greyhound racing are all covered, and the authors (including Hsinchun Chen, one of the most esteemed and well-known experts in data mining in the world) present the latest research, developments, software available, and applications for each sport. They even examine the hidden patterns in gaming and wagering, along with the most common systems for wager analysis.

This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates such as classical local averaging estimates including kernel, partitioning and nearest neighbor estimates, least squares estimates using splines, neural networks and radial basis function networks, penalized least squares estimates, local polynomial kernel estimates, and orthogonal series estimates. The emphasis is on distribution-free properties of the estimates. Most consistency results are valid for all distributions of the data. Whenever it is not possible to derive distribution-free results, as in the case of the rates of convergence, the emphasis is on results which require as few constrains on distributions as possible, on distribution-free inequalities, and on adaptation. The relevant mathematical theory is systematically developed and requires only a basic knowledge of probability theory. The book will be a valuable reference for anyone interested in nonparametric regression and is a rich source of many useful mathematical techniques widely scattered in the literature. In particular, the book introduces the reader to empirical process theory, martingales and approximation properties of neural networks.

The evolution of systems in random media is a broad and fruitful field for the applica tions of different mathematical methods and theories. This evolution can be character ized by a semigroup property. In the abstract form, this property is given by a semigroup of operators in a normed vector (Banach) space. In the practically boundless variety of mathematical models of the evolutionary systems, we have chosen the semi-Markov ran dom evolutions as an object of our consideration. The definition of the evolutions of this type is based on rather simple initial assumptions. The random medium is described by the Markov renewal processes or by the semi Markov processes. The local characteristics of the system depend on the state of the ran dom medium. At the same time, the evolution of the system does not affect the medium. Hence, the semi-Markov random evolutions are described by two processes, namely, by the switching Markov renewal process, which describes the changes of the state of the external random medium, and by the switched process, i.e., by the semigroup of oper ators describing the evolution of the system in the semi-Markov random medium."

For surveys involving sensitive questions, randomized response techniques (RRTs) and other indirect questions are helpful in obtaining survey responses while maintaining the privacy of the respondents. Written by one of the leading experts in the world on RR, Randomized Response and Indirect Questioning Techniques in Surveys describes the current state of RR as well as emerging developments in the field. The author also explains how to extend RR to situations employing unequal probability sampling. While the theory of RR has grown phenomenally, the area has not kept pace in practice. Covering both theory and practice, the book first discusses replacing a direct response (DR) with an RR in a simple random sample with replacement (SRSWR). It then emphasizes how the application of RRTs in the estimation of attribute or quantitative features is valid for selecting respondents in a general manner. The author examines different ways to treat maximum likelihood estimation; covers optional RR devices, which provide alternatives to compulsory randomized response theory; and presents RR techniques that encompass quantitative variables, including those related to stigmatizing characteristics. He also gives his viewpoint on alternative RR techniques, including the item count technique, nominative technique, and three-card method.

This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises' views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises' definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the actual world of experiments'. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper's concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics.

This monograph deals with spatially dependent nonstationary time series in a way accessible to both time series econometricians wanting to understand spatial econometics, and spatial econometricians lacking a grounding in time series analysis. After charting key concepts in both time series and spatial econometrics, the book discusses how the spatial connectivity matrix can be estimated using spatial panel data instead of assuming it to be exogenously fixed. This is followed by a discussion of spatial nonstationarity in spatial cross-section data, and a full exposition of non-stationarity in both single and multi-equation contexts, including the estimation and simulation of spatial vector autoregression (VAR) models and spatial error correction (ECM) models. The book reviews the literature on panel unit root tests and panel cointegration tests for spatially independent data, and for data that are strongly spatially dependent. It provides for the first time critical values for panel unit root tests and panel cointegration tests when the spatial panel data are weakly or spatially dependent. The volume concludes with a discussion of incorporating strong and weak spatial dependence in non-stationary panel data models. All discussions are accompanied by empirical testing based on a spatial panel data of house prices in Israel.

This introductory textbook is designed for a one-semester course on queueing theory that does not require a course on stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. This edition includes additional topics in methodology and applications. Key features: * An introductory chapter including a historical account of the growth of queueing theory in more than 100 years. * A modeling-based approach with emphasis on identification of models * Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics. * A chapter on matrix-analytic method as an alternative to the traditional methods of analysis of queueing systems. * A comprehensive treatment of statistical inference for queueing systems. * Modeling exercises and review exercises when appropriate. The second edition of An Introduction of Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research. "...This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books." - Assam Statistical Review of the first edition

A recent development in SDC-related problems is the establishment of intelligent SDC models and the intensive use of LMI-based convex optimization methods. Within this theoretical framework, control parameter determination can be designed and stability and robustness of closed-loop systems can be analyzed. This book describes the new framework of SDC system design and provides a comprehensive description of the modelling of controller design tools and their real-time implementation. It starts with a review of current research on SDC and moves on to some basic techniques for modelling and controller design of SDC systems. This is followed by a description of controller design for fixed-control-structure SDC systems, PDF control for general input- and output-represented systems, filtering designs, and fault detection and diagnosis (FDD) for SDC systems. Many new LMI techniques being developed for SDC systems are shown to have independent theoretical significance for robust control and FDD problems.

This book covers several bases at once. It is useful as a textbook for a second course in experimental optimization techniques for industrial production processes. In addition, it is a superb reference volume for use by professors and graduate students in Industrial Engineering and Statistics departments. It will also be of huge interest to applied statisticians, process engineers, and quality engineers working in the electronics and biotech manufacturing industries. In all, it provides an in-depth presentation of the statistical issues that arise in optimization problems, including confidence regions on the optimal settings of a process, stopping rules in experimental optimization, and more.

Testing for a Unit Root is now an essential part of time series analysis but the literature on the topic is so large that knowing where to start is difficult even for the specialist. This book provides a way into the techniques of unit root testing, explaining the pitfalls and nonstandard cases, using practical examples and simulation analysis.

From the Foreword: The chief aim of this book is to present the reader with an integrated system of methods dealing with geographical statistics (geostatistics') and their applications. It sums up developments based on the vast experience accumulated by Professor Bachi over several decades of research. Interest in the quantitative locational aspects of geography and in the common ground of geography and statistics has grown rapidly, involving an ever-increasing spectrum of scientific disciplines ... the present volume will fill a genuine need - as a textbook, as a reference work, and as a practical aid for geographers, applied statisticians, demographers, ecologists, regional planners, economists, professional staff of official statistical agencies, and others.' - E. Peritz, G. Nathan, N. Kadmon.

'Et moi, ..., si. j'avail su comment en revenir. One service mathematics has rendered be human race. It has put common sense back jc n'y scrais point a1U: where it belongs, on the topmost sbelf next Jules Verne to \be dusty canister labelled 'discarded non- TIle series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities 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 bas 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 book is devoted to the study of univariate distributions appropriate for the analyses of data known to be nonnegative. The book includes much material from reliability theory in engineering and survival analysis in medicine.

The aim of this book is to provide a strong theoretical support for understanding and analyzing the behavior of evolutionary algorithms, as well as for creating a bridge between probability, set-oriented numerics and evolutionary computation. The volume encloses a collection of contributions that were presented at the EVOLVE 2011 international workshop, held in Luxembourg, May 25-27, 2011, coming from invited speakers and also from selected regular submissions. The aim of EVOLVE is to unify the perspectives offered by probability, set oriented numerics and evolutionary computation. EVOLVE focuses on challenging aspects that arise at the passage from theory to new paradigms and practice, elaborating on the foundations of evolutionary algorithms and theory-inspired methods merged with cutting-edge techniques that ensure performance guarantee factors. EVOLVE is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. The chapters enclose challenging theoretical findings, concrete optimization problems as well as new perspectives. By gathering contributions from researchers with different backgrounds, the book is expected to set the basis for a unified view and vocabulary where theoretical advancements may echo in different domains.

"Statistical Modeling, Analysis and Management of Fuzzy Data," or SMFD for short, is an important contribution to a better understanding of a basic issue -an issue which has been controversial, and still is though to a lesser degree. In substance, the issue is: are fuzziness and randomness distinct or coextensive facets of uncertainty? Are the theories of fuzziness and random ness competitive or complementary? In SMFD, these and related issues are addressed with rigor, authority and insight by prominent contributors drawn, in the main, from probability theory, fuzzy set theory and data analysis com munities. First, a historical perspective. The almost simultaneous births -close to half a century ago-of statistically-based information theory and cybernetics were two major events which marked the beginning of the steep ascent of probability theory and statistics in visibility, influence and importance. I was a student when information theory and cybernetics were born, and what is etched in my memory are the fascinating lectures by Shannon and Wiener in which they sketched their visions of the coming era of machine intelligence and automation of reasoning and decision processes. What I heard in those lectures inspired one of my first papers (1950) "An Extension of Wiener's Theory of Prediction," and led to my life-long interest in probability theory and its applications to information processing, decision analysis and control."

In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, "In God we trust; all others must bring data."
This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem.Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings.

This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics. "

A "health disparity" refers to a higher burden of illness, injury, disability, or mortality experienced by one group relative to another. These disparities may be due to many factors including age, income, race, etc. This book will focus on their estimation, ranging from classical approaches including the quantification of a disparity, to more formal modelling, to modern approaches involving more flexible computational approaches. Features: * Presents an overview of methods and applications of health disparity estimation * First book to synthesize research in this field in a unified statistical framework * Covers classical approaches, and builds to more modern computational techniques * Includes many worked examples and case studies using real data * Discusses available software for estimation The book is designed primarily for researchers and graduate students in biostatistics, data science, and computer science. It will also be useful to many quantitative modelers in genetics, biology, sociology, and epidemiology.

Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.

This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." We would like to thank the scientific organizers: John Goutsias (Johns Hopkins University), Ronald P.S. Mahler (Lockheed Martin), and Hung T. Nguyen (New Mexico State University) for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the Army Research Office (ARO), the Office ofNaval Research (0NR), and the Eagan, MinnesotaEngineering Center ofLockheed Martin Tactical Defense Systems, whose financial support made the summer program possible. Avner Friedman Robert Gulliver v PREFACE "Later generations will regard set theory as a disease from which one has recovered. " - Henri Poincare Random set theory was independently conceived by D.G. Kendall and G. Matheron in connection with stochastic geometry. It was however G.

This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.

Showcases the excellent data science environment in Python. Provides examples for readers to replicate, adapt, extend, and improve. Covers the crucial knowledge needed by geographic data scientist.

Most applications generate large datasets, like social networking and social influence programs, smart cities applications, smart house environments, Cloud applications, public web sites, scientific experiments and simulations, data warehouse, monitoring platforms, and e-government services. Data grows rapidly, since applications produce continuously increasing volumes of both unstructured and structured data. Large-scale interconnected systems aim to aggregate and efficiently exploit the power of widely distributed resources. In this context, major solutions for scalability, mobility, reliability, fault tolerance and security are required to achieve high performance and to create a smart environment. The impact on data processing, transfer and storage is the need to re-evaluate the approaches and solutions to better answer the user needs. A variety of solutions for specific applications and platforms exist so a thorough and systematic analysis of existing solutions for data science, data analytics, methods and algorithms used in Big Data processing and storage environments is significant in designing and implementing a smart environment. Fundamental issues pertaining to smart environments (smart cities, ambient assisted leaving, smart houses, green houses, cyber physical systems, etc.) are reviewed. Most of the current efforts still do not adequately address the heterogeneity of different distributed systems, the interoperability between them, and the systems resilience. This book will primarily encompass practical approaches that promote research in all aspects of data processing, data analytics, data processing in different type of systems: Cluster Computing, Grid Computing, Peer-to-Peer, Cloud/Edge/Fog Computing, all involving elements of heterogeneity, having a large variety of tools and software to manage them. The main role of resource management techniques in this domain is to create the suitable frameworks for development of applications and deployment in smart environments, with respect to high performance. The book focuses on topics covering algorithms, architectures, management models, high performance computing techniques and large-scale distributed systems.

Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups.

The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.