Bücher der Reihe Springer Texts in Statistics

This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "e;interesting but not essential"e; (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "e;INE"e;. We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.

<div style="e;MARGIN: 0in 0in 0pt; LINE-HEIGHT: normal"e;>Financial engineers have access to enormous quantities of data but need powerful methods for extracting quantitative information, particularly about volatility and risks. Key features of this textbook are: illustration of concepts with financial markets and economic data, R Labs with real-data exercises, and integration of graphical and analytic methods for modeling and diagnosing modeling errors. Despite some overlap with the author's undergraduate textbook <em>Statistics and Finance: An Introduction</em>, this book differs from that earlier volume in several important aspects: it is graduate-level; computations and graphics are done in R; and many advanced topics are covered, for example, multivariate distributions, copulas, Bayesian computations, VaR and expected shortfall, and cointegration. </div><div style="e;MARGIN: 0in 0in 0pt; LINE-HEIGHT: normal"e;>The prerequisites are basic statistics and probability, matrices and linear algebra, and calculus.</div><div style="e;MARGIN: 0in 0in 0pt; LINE-HEIGHT: normal"e;>Some exposure to finance is helpful.</div>

This book is a novel exposition of the traditional workhorses of statistics: analysis of variance and regression. The key feature is that these tools are viewed in their natural mathematical setting, the geometry of finite dimensions. The Authors To introduce ourselves, Dave Saville is a practicing statistician working in agricultural research; Graham Wood is a university lecturer involved in the teaching of statistical methods. Each of us has worked for sixteen years in our current field. Features of the Book People like pictures. One picture can present a set of ideas at a glance, while a series of pictures, each building on the last, can unify a wealth of ideas. Such a series we present in this text by means of a systematic geometric approach to the presentation of the theory of basic statistical methods. This approach fills the void between the traditional extremes of the "e;cookbook"e; approach and the "e;matrix algebra"e; approach, providing an elementary but at the same time rigorous view of the subject. It combines the virtues of the traditional methods, while avoiding their vices.

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.

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.

As an introductory textbook on the analysis of variance or a reference for the researcher, this text stresses applications rather than theory, but gives enough theory to enable the reader to apply the methods intelligently rather than mechanically. Comprehensive, and covering the important techniques in the field, including new methods of post hoc testing. The relationships between different research designs are emphasized, and these relationships are exploited to develop general principles which are generalized to the analyses of a large number of seemingly differentdesigns. Primarily for graduate students in any field where statistics are used.

This book was written to myself at about the time I began graduate studies in anthropology-the sort of thing a Samuel Beckett character might do. It is about the conduct of research. In a very real sense the purpose is partially to compensate for the inadequacies of my professors. Perhaps this is what education is about. The effort has not been an unqualified success, but it has been extremely gratifying. I was trained in anthropology. After completing the Ph. D. I went to Stanford on a post-doctoral fellowship. At the time, this was a novelty and the depart- ment was not prepared for such a thing. To stay occupied I began attending lectures, seminars, and discussion groups in mathematics and statistics. This was about the luckiest choice I ever made. The excitement was easily as intense as that which I experienced upon encountering anthropology. On one oc- casion I innocently and independently proved a theorem that had first been done 2000 years earlier. It is currently used as an exercise in high school mathematics so it is neither difficult nor arcane. Learning all this did not tarnish my sense of discovery. (On reflection I am puzzled by my failure to have seen all this "e;beauty"e; when I was exposed to it as an undergraduate. The unparalleled excellence of the Stanford program was undoubtedly responsible for my belated conversion.

Portraying data graphically certainly contributes toward a clearer and more penetrative understanding of data and also makes sophisticated statistical data analyses more marketable. This realization has emerged from many years of experience in teaching students, in research, and especially from engaging in statistical consulting work in a variety of subject fields. Consequently, we were somewhat surprised to discover that a comprehen- sive, yet simple presentation of graphical exploratory techniques for the data analyst was not available. Generally books on the subject were either too incomplete, stopping at a histogram or pie chart, or were too technical and specialized and not linked to readily available computer programs. Many of these graphical techniques have furthermore only recently appeared in statis- tical journals and are thus not easily accessible to the statistically unsophis- ticated data analyst. This book, therefore, attempts to give a sound overview of most of the well-known and widely used methods of analyzing and portraying data graph- ically. Throughout the book the emphasis is on exploratory techniques. Real- izing the futility of presenting these methods without the necessary computer programs to actually perform them, we endeavored to provide working com- puter programs in almost every case. Graphic representations are illustrated throughout by making use of real-life data. Two such data sets are frequently used throughout the text. In realizing the aims set out above we avoided intricate theoretical derivations and explanations but we nevertheless are convinced that this book will be of inestimable value even to a trained statistician.

Reliability analysis is concerned with the analysis of devices and systems whose individual components are prone to failure. This textbook presents an introduction to reliability analysis of repairable and non-repairable systems. It is based on courses given to both undergraduate and graduate students of engineering and statistics as well as in workshops for professional engineers and scientists. As aresult, the book concentrates on the methodology of the subject and on understanding theoretical results rather than on its theoretical development. An intrinsic aspect of reliability analysis is that the failure of components is best modelled using techniques drawn from probability and statistics. Professor Zacks covers all the basic concepts required from these subjects and covers the main modern reliability analysis techniques thoroughly. These include: the graphical analysis of life data, maximum likelihood estimation and bayesian likelihood estimation. Throughout the emphasis is on the practicalities of the subject with numerous examples drawn from industrial and engineering settings.

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.

All students and professionals in statistics should refer to this volume as it is a handy reference source for statistical formulas and information on basic probability distributions. It contains carefully designed and well laid out tables for standard statistical distributions (including Binomial, Poisson, Normal, and Chi-squared). In addition, there are several tables of Critical Values for various statistics tests.

This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..

Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models.

This textbook provides a step-by-step introduction to the tools and principles of high-dimensional statistics. The book covers the theory and practice of high-dimensional linear regression, graphical models, and inference, ensuring readers have a smooth start in the field. It also offers suggestions for further reading.

This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.

In its revised new edition, this book covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales and mathematical finance. Offers many examples and more than 300 carefully chosen exercises for better understanding.