Multivariate Density Estimation

Author: David W. Scott
Publisher: John Wiley & Sons
ISBN: 9781118575536
Release Date: 2015-03-12
Genre: Mathematics

Clarifies modern data analysis through nonparametric density estimation for a complete working knowledge of the theory and methods Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis. The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analysis. Continuing to illustrate the major concepts in the context of the classical histogram, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition also features: Over 150 updated figures to clarify theoretical results and to show analyses of real data sets An updated presentation of graphic visualization using computer software such as R A clear discussion of selections of important research during the past decade, including mixture estimation, robust parametric modeling algorithms, and clustering More than 130 problems to help readers reinforce the main concepts and ideas presented Boxed theorems and results allowing easy identification of crucial ideas Figures in color in the digital versions of the book A website with related data sets Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The Second Edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions.

Density Estimation for Statistics and Data Analysis

Author: Bernard. W. Silverman
Publisher: Routledge
ISBN: 9781351456166
Release Date: 2018-02-19
Genre: Mathematics

Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician. The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text. Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.

Encyclopedia of Environmetrics

Author: Abdel H. El-Shaarawi
Publisher: John Wiley & Sons
ISBN: 0471899976
Release Date: 2002
Genre: Mathematics

A comprehensive overview of environmetric research and its applications... Environmetrics covers the development and application of quantitative methods in the environmental sciences. It provides essential tools for understanding, predicting, and controlling the impacts of agents, both man-made and natural, which affect the environment. Basic and applied research in this area covers a broad range of topics. Primary among these are the quantitative sciences, such as statistics, probability and applied mathematics, chemometrics, and econometrics. Applications are also important, for example in, ecology and environmental biology, public health, atmospheric science, geology, engineering, risk management, and regulatory/governmental policy amongst others. * Divided into 12 sections, the Encyclopedia brings together over 600 detailed articles which have been carefully selected and reviewed through the collaborative efforts of the Editors-in-Chief and the appropriate Section Editor * Presented in alphabetical order all the articles will include an explanatory introduction, extensive cross-referencing and an up-to-date bibliography providing literature references for further reading. Presenting state of the art information in a readable, highly accessible style, the scope and coverage provided by the Encyclopedia of Environmetrics will ensure its place as the landmark reference for the many scientists, educators, and decision-makers working across this multidisciplinary field. An essential reference tool for university libraries, research laboratories, government institutions and consultancies concerned with the environmental sciences, the Encyclopedia of Environmetrics brings together for the first time, comprehensive coverage of the full range of topics, techniques and applications covered by this multidisciplinary field. There is currently no central reference source which addresses the needs of this multidisciplinary community. This new Encyclopedia will fill this gap by providing a comprehensive source of relevant fundamental concepts in environmetric research, development and applications for statisticians, mathematicians, economists, environmentalists, ecologist, government officials and policy makers.

Nonparametric Functional Data Analysis

Author: Frédéric Ferraty
Publisher: Springer Science & Business Media
ISBN: 9780387366203
Release Date: 2006-11-22
Genre: Mathematics

Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Smoothing of Multivariate Data

Author: Jussi Klemel?
Publisher: John Wiley & Sons
ISBN: 0470425660
Release Date: 2009-09-04
Genre: Mathematics

An applied treatment of the key methods and state-of-the-art tools for visualizing and understanding statistical data Smoothing of Multivariate Data provides an illustrative and hands-on approach to the multivariate aspects of density estimation, emphasizing the use of visualization tools. Rather than outlining the theoretical concepts of classification and regression, this book focuses on the procedures for estimating a multivariate distribution via smoothing. The author first provides an introduction to various visualization tools that can be used to construct representations of multivariate functions, sets, data, and scales of multivariate density estimates. Next, readers are presented with an extensive review of the basic mathematical tools that are needed to asymptotically analyze the behavior of multivariate density estimators, with coverage of density classes, lower bounds, empirical processes, and manipulation of density estimates. The book concludes with an extensive toolbox of multivariate density estimators, including anisotropic kernel estimators, minimization estimators, multivariate adaptive histograms, and wavelet estimators. A completely interactive experience is encouraged, as all examples and figurescan be easily replicated using the R software package, and every chapter concludes with numerous exercises that allow readers to test their understanding of the presented techniques. The R software is freely available on the book's related Web site along with "Code" sections for each chapter that provide short instructions for working in the R environment. Combining mathematical analysis with practical implementations, Smoothing of Multivariate Data is an excellent book for courses in multivariate analysis, data analysis, and nonparametric statistics at the upper-undergraduate and graduatelevels. It also serves as a valuable reference for practitioners and researchers in the fields of statistics, computer science, economics, and engineering.

Introductory Statistics

Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 9780128043615
Release Date: 2017-01-26
Genre: Mathematics

Introductory Statistics, Fourth Edition, reviews statistical concepts and techniques in a manner that will teach students not only how and when to utilize the statistical procedures developed, but also how to understand why these procedures should be used. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, an explanation of intuition, and the ideas behind the statistical methods. Concepts are motivated, illustrated, and explained in a way that attempts to increase one's intuition. To quote from the preface, it is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data. Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions, and examples. Applications and examples refer to real-world issues, such as gun control, stock price models, health issues, driving age limits, school admission ages, use of helmets, sports, scientific fraud, and many others. Examples relating to data mining techniques using the number of Google queries or Twitter tweets are also considered. For this fourth edition, new topical coverage includes sections on Pareto distribution and the 80-20 rule, Benford's law, added material on odds and joint distributions and correlation, logistic regression, A-B testing, and more modern (big data) examples and exercises. Includes new section on Pareto distribution and the 80-20 rule, Benford’s law, odds, joint distribution and correlation, logistic regression, A-B testing, and examples from the world of analytics and big data Comprehensive edition that includes the most commonly used statistical software packages (SAS, SPSS, Minitab), ISM, SSM, and an online graphing calculator manual Presents a unique, historical perspective, profiling prominent statisticians and historical events to motivate learning by including interest and context Provides exercises and examples that help guide the student towards indpendent learning using real issues and real data, e.g. stock price models, health issues, gender issues, sports, and scientific fraud

Operational Risk

Author: Harry H. Panjer
Publisher: John Wiley & Sons
ISBN: 9780470051306
Release Date: 2006-10-13
Genre: Business & Economics

Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.

Nonparametric Econometrics

Author: Qi Li
Publisher: Princeton University Press
ISBN: 9781400841066
Release Date: 2011-10-09
Genre: Business & Economics

Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data--nominal and ordinal--in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types--continuous, nominal, and ordinal--within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.

Longitudinal Data Analysis

Author: Donald Hedeker
Publisher: John Wiley & Sons
ISBN: 9780470036471
Release Date: 2006-05-12
Genre: Mathematics

Longitudinal data analysis for biomedical and behavioral sciences This innovative book sets forth and describes methods for the analysis of longitudinaldata, emphasizing applications to problems in the biomedical and behavioral sciences. Reflecting the growing importance and use of longitudinal data across many areas of research, the text is designed to help users of statistics better analyze and understand this type of data. Much of the material from the book grew out of a course taught by Dr. Hedeker on longitudinal data analysis. The material is, therefore, thoroughly classroom tested and includes a number of features designed to help readers better understand and apply the material. Statistical procedures featured within the text include: * Repeated measures analysis of variance * Multivariate analysis of variance for repeated measures * Random-effects regression models (RRM) * Covariance-pattern models * Generalized-estimating equations (GEE) models * Generalizations of RRM and GEE for categorical outcomes Practical in their approach, the authors emphasize the applications of the methods, using real-world examples for illustration. Some syntax examples are provided, although the authors do not generally focus on software in this book. Several datasets and computer syntax examples are posted on this title's companion Web site. The authors intend to keep the syntax examples current as new versions of the software programs emerge. This text is designed for both undergraduate and graduate courses in longitudinal data analysis. Instructors can take advantage of overheads and additional course materials available online for adopters. Applied statisticians in biomedicine and the social sciences can also use the book as a convenient reference.

Applied Linear Regression

Author: Sanford Weisberg
Publisher: John Wiley & Sons
ISBN: 9781118594858
Release Date: 2013-11-25
Genre: Mathematics

Praise for the Third Edition "...this is an excellent book which could easily be used as a course text..." —International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illustrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. While maintaining the accessible appeal of each previous edition,Applied Linear Regression, Fourth Edition features: Graphical methods stressed in the initial exploratory phase, analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple and complex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, and variance assumptions Updated methodology, such as bootstrapping, cross-validation binomial and Poisson regression, and modern model selection methods Applied Linear Regression, Fourth Edition is an excellent textbook for upper-undergraduate and graduate-level students, as well as an appropriate reference guide for practitioners and applied statisticians in engineering, business administration, economics, and the social sciences.

Regression Analysis by Example

Author: Samprit Chatterjee
Publisher: John Wiley & Sons
ISBN: 9780470055458
Release Date: 2006-10-20
Genre: Mathematics

The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Robust Statistics

Author: Frank R. Hampel
Publisher: John Wiley & Sons
ISBN: 9781118150689
Release Date: 2011-09-20
Genre: Mathematics

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "This is a nice book containing a wealth of information, much of it due to the authors. . . . If an instructor designing such a course wanted a textbook, this book would be the best choice available. . . . There are many stimulating exercises, and the book also contains an excellent index and an extensive list of references." —Technometrics "[This] book should be read carefully by anyone who is interested in dealing with statistical models in a realistic fashion." —American Scientist Introducing concepts, theory, and applications, Robust Statistics is accessible to a broad audience, avoiding allusions to high-powered mathematics while emphasizing ideas, heuristics, and background. The text covers the approach based on the influence function (the effect of an outlier on an estimater, for example) and related notions such as the breakdown point. It also treats the change-of-variance function, fundamental concepts and results in the framework of estimation of a single parameter, and applications to estimation of covariance matrices and regression parameters.

Time Series

Author: Ngai Hang Chan
Publisher: John Wiley & Sons
ISBN: 9781118030714
Release Date: 2011-01-25
Genre: Mathematics

A new edition of the comprehensive, hands-on guide to financial time series, now featuring S-Plus® and R software Time Series: Applications to Finance with R and S-Plus®, Second Edition is designed to present an in-depth introduction to the conceptual underpinnings and modern ideas of time series analysis. Utilizing interesting, real-world applications and the latest software packages, this book successfully helps readers grasp the technical and conceptual manner of the topic in order to gain a deeper understanding of the ever-changing dynamics of the financial world. With balanced coverage of both theory and applications, this Second Edition includes new content to accurately reflect the current state-of-the-art nature of financial time series analysis. A new chapter on Markov Chain Monte Carlo presents Bayesian methods for time series with coverage of Metropolis-Hastings algorithm, Gibbs sampling, and a case study that explores the relevance of these techniques for understanding activity in the Dow Jones Industrial Average. The author also supplies a new presentation of statistical arbitrage that includes discussion of pairs trading and cointegration. In addition to standard topics such as forecasting and spectral analysis, real-world financial examples are used to illustrate recent developments in nonstandard techniques, including: Nonstationarity Heteroscedasticity Multivariate time series State space modeling and stochastic volatility Multivariate GARCH Cointegration and common trends The book's succinct and focused organization allows readers to grasp the important ideas of time series. All examples are systematically illustrated with S-Plus® and R software, highlighting the relevance of time series in financial applications. End-of-chapter exercises and selected solutions allow readers to test their comprehension of the presented material, and a related Web site features additional data sets. Time Series: Applications to Finance with R and S-Plus® is an excellent book for courses on financial time series at the upper-undergraduate and beginning graduate levels. It also serves as an indispensible resource for practitioners working with financial data in the fields of statistics, economics, business, and risk management.

Nonparametric Statistical Methods

Author: Myles Hollander
Publisher: John Wiley & Sons
ISBN: 9781118553299
Release Date: 2013-11-25
Genre: Mathematics

Praise for the Second Edition “This book should be an essential part of the personal library of every practicing statistician.”—Technometrics Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation. Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. In addition, the Third Edition features: The use of the freely available R software to aid in computation and simulation, including many new R programs written explicitly for this new edition New chapters that address density estimation, wavelets, smoothing, ranked set sampling, and Bayesian nonparametrics Problems that illustrate examples from agricultural science, astronomy, biology, criminology, education, engineering, environmental science, geology, home economics, medicine, oceanography, physics, psychology, sociology, and space science Nonparametric Statistical Methods, Third Edition is an excellent reference for applied statisticians and practitioners who seek a review of nonparametric methods and their relevant applications. The book is also an ideal textbook for upper-undergraduate and first-year graduate courses in applied nonparametric statistics.