Welcome to new territory: A course in probability models and statistical inference. The concept of probability is not new to you of course. You've encountered it since childhood in games of chance-card games, for example, or games with dice or coins. And you know about the "90% chance of rain" from weather reports. But once you get beyond simple expressions of probability into more subtle analysis, it's new territory. And very foreign territory it is. You must have encountered reports of statistical results in voter sur veys, opinion polls, and other such studies, but how are conclusions from those studies obtained? How can you interview just a few voters the day before an election and still determine fairly closely how HUN DREDS of THOUSANDS of voters will vote? That's statistics. You'll find it very interesting during this first course to see how a properly designed statistical study can achieve so much knowledge from such drastically incomplete information. It really is possible-statistics works! But HOW does it work? By the end of this course you'll have understood that and much more. Welcome to the enchanted forest.

A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate distributions from first principles. After a chapter on the multivariate normal distribution reviewing the classical parametric theory, methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests. Finally, the powerful self-consistency principle is used to introduce principal components as a method of approximation, rounded off by a chapter on finite mixture analysis.

This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

This book introduces several topics related to linear model theory, including: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. This second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subjects and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure.

The primary focus here is on log-linear models for contingency tables, but in this second edition, greater emphasis has been placed on logistic regression. The book explores topics such as logistic discrimination and generalised linear models, and builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. It also carefully examines the differences in model interpretations and evaluations that occur due to the discrete nature of the data. Sample commands are given for analyses in SAS, BMFP, and GLIM, while numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. Throughoutthe book, the treatment is designed for students with prior knowledge of analysis of variance and regression.

This text provides the reader with a single book where they can find accounts of a number of up-to-date issues in nonparametric inference. The book is aimed at Masters or PhD level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. It covers a wide range of topics including the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book’s dual approach includes a mixture of methodology and theory.

Categorical data arise often in many fields, including biometrics, economics, management, manufacturing, marketing, psychology, and sociology. This book provides an introduction to the analysis of such data. The coverage is broad, using the loglinear Poisson regression model and logistic binomial regression models as the primary engines for methodology. Topics covered include count regression models, such as Poisson, negative binomial, zero-inflated, and zero-truncated models; loglinear models for two-dimensional and multidimensional contingency tables, including for square tables and tables with ordered categories; and regression models for two-category (binary) and multiple-category target variables, such as logistic and proportional odds models. All methods are illustrated with analyses of real data examples, many from recent subject area journal articles. These analyses are highlighted in the text, and are more detailed than is typical, providing discussion of the context and background of the problem, model checking, and scientific implications. More than 200 exercises are provided, many also based on recent subject area literature. Data sets and computer code are available at a web site devoted to the text. Adopters of this book may request a solutions manual from: textbook@springer-ny.com. From the reviews: "Jeff Simonoff's book is at the top of the heap of categorical data analysis textbooks...The examples are superb. Student reactions in a class I taught from this text were uniformly positive, particularly because of the examples and exercises. Additional materials related to the book, particularly code for S-Plus, SAS, and R, useful for analysis of examples, can be found at the author's Web site at New York University. I liked this book for this reason, and recommend it to you for pedagogical purposes." (Stanley Wasserman, The American Statistician, August 2006, Vol. 60, No. 3) "The book has various noteworthy features. The examples used are from a variety of topics, including medicine, economics, sports, mining, weather, as well as social aspects like needle-exchange programs. The examples motivate the theory and also illustrate nuances of data analytical procedures. The book also incorporates several newer methods for analyzing categorical data, including zero-inflated Poisson models, robust analysis of binomial and poisson models, sandwich estimators, multinomial smoothing, ordinal agreement tables...this is definitely a good reference book for any researcher working with categorical data." Technometrics, May 2004 "This guide provides a practical approach to the appropriate analysis of categorical data and would be a suitable purchase for individuals with varying levels of statistical understanding." Paediatric and Perinatal Epidemiology, 2004, 18 "This book gives a fresh approach to the topic of categorical data analysis. The presentation of the statistical methods exploits the connection to regression modeling with a focus on practical features rather than formal theory...There is much to learn from this book. Aside from the ordinary materials such as association diagrams, Mantel-Haenszel estimators, or overdispersion, the reader will also find some less-often presented but interesting and stimulating topics...[T]his is an excellent book, giving an up-to-date introduction to the wide field of analyzing categorical data." Biometrics, September 2004 "...It is of great help to data analysts, practitioners and researchers who deal with categorical data and need to get a necessary insight into the methods of analysis as well as practical guidelines for solving problems." International Journal of General Systems, August 2004 "The author has succeeded in writing a useful and readable textbook combining most of general theory and practice of count data." Kwantitatieve Methoden "The book especially stresses how to analyze and interpret data...In fact, the highly detailed multi-page descriptions of analysis and interpretation make the book stand out." Mathematical Geology, February 2005 "Overall, this is a competent and detailed text that I would recommend to anyone dealing with the analysis of categorical data." Journal of the Royal Statistical Society "This important work allows for clear analogies between the well-known linear models for Gaussian data and categorical data problems. ... Jeffrey Simonoff’s Analyzing Categorical Data provides an introduction to many of the important ideas and methods for understanding counted data and tables of counts. ... Some readers will find Simonoff’s style very much to their liking due to reliance on extended real data examples to illuminate ideas. ... I think the extensive examples will appeal to most students." (Sanford Weisberg, SIAM Review, Vol. 47 (4), 2005) "It is clear that the focus of Simonoff’s book is different from other books on categorical data analysis. ... As an introductory textbook, the book is comprehensive enough since all basic topics in categorical data analysis are discussed. ... I think Simonoff’s book is a valuable addition to the literature because it discusses important models for counts ... ." (Jeroen K. Vermunt, Statistics in Medicine, Vol. 24, 2005) "The author based this book on his notes for a class with a very diverse pool of students. The material is presented in such a way that a very heterogeneous group of students could grasp it. All methods are illustrated with analyses of real data examples. The author provides a detailed discussion of the context and background of the problem. ... The book is very interesting and can be warmly recommended to people working with categorical data." (EMS - European Mathematical Society Newsletter, December, 2004) "Categorical data arise often in many fields ... . This book provides an introduction to the analysis of such data. ... All methods are illustrated with analyses of real data examples, many from recent subject-area journal articles. These analyses are highlighted in the text and are more detailed than is typical ... . More than 200 exercises are provided, including many based on recent subject-area literature. Data sets and computer code are available at a Web site devoted to this text." (T. Postelnicu, Zentralblatt MATH, Vol. 1028, 2003) "This book grew out of notes prepared by the author for classes in categorical data analysis. The presentation is fresh and compelling to read. Regression ideas are used to motivate the modelling presented. The book focuses on applying methods to real problems; many of these will be novel to readers of statistics texts ... . All chapters end with a section providing references to books or articles for the inquiring reader." (C.M. O’Brien, Short Book Reviews, Vol. 23 (3), 2003)

This book has exerted a continuing appeal since its original publication in 1970. It develops the theory of probability from axioms on the expectation functional rather than on probability measure, demonstrates that the standard theory unrolls more naturally and economically this way, and that applications of real interest can be addressed almost immediately. A secondary aim of the original text was to introduce fresh examples and convincing applications, and that aim is continued in this edition, a general revision plus the addition of chapters giving an economical introduction to dynamic programming, that is then applied to the allocation problems represented by portfolio selection and the multi-armed bandit. The investment theme is continued with a critical investigation of the concept of risk-free'trading and the associated Black-Sholes formula, while another new chapter develops the basic ideas of large deviations. The book may be seen as an introduction to probability for students with a basic mathematical facility, covering the standard material, but different in that it is unified by its theme and covers an unusual range of modern applications.

This book offers a modern and accessible introduction to Statistical Inference, the science of inferring key information from data. Aimed at beginning undergraduate students in mathematics, it presents the concepts underpinning frequentist statistical theory. Written in a conversational and informal style, this concise text concentrates on ideas and concepts, with key theorems stated and proved. Detailed worked examples are included and each chapter ends with a set of exercises, with full solutions given at the back of the book. Examples using R are provided throughout the book, with a brief guide to the software included. Topics covered in the book include: sampling distributions, properties of estimators, confidence intervals, hypothesis testing, ANOVA, and fitting a straight line to paired data. Based on the author's extensive teaching experience, the material of the book has been honed by student feedback for over a decade. Assuming only some familiarity with elementary probability, this textbook has been devised for a one semester first course in statistics.