Author: William Feller

Publisher: N.A

ISBN: N.A

Category: Probabilities

Page: 509

View: 1808

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# An Introduction to Probability Theory and Its Applications

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# An Introduction to Probability Theory and Its Applications

# Unit Root Tests in Time Series Volume 1

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Probabilities

Author: William Feller

Publisher: N.A

ISBN: N.A

Category: Probabilities

Page: 509

View: 1808

Problems after each chapterSocial Science

*Anwendung statistischer Methoden*

Author: Lothar Sachs

Publisher: Springer-Verlag

ISBN: 3662057484

Category: Social Science

Page: 553

View: 1952

Die Neuauflage bot Gelegenheit zu Berichtigungen, Vereinfa chungen, Präzisierungen und einigen Ergänzungen. Wesentlich umfangreichere Ergänzungen, Einfügungen und erweiterteN eu fassungen, kamen, da der Rahmen nicht vorgegeben war, der englischen Übersetzung (New York 1982) zugute; dies gilt auch für den TabellenteiL Eine knappe Übersicht bietet mein Ta schenbuch "Statistische Methoden" (5. Aufl. 1982). Den Damen und Herren des Springer-Verlages sei für ihr bereitwilliges Eingehen auf alle Wünsche des Autors besonders gedankt. Weiterhin bin ich für Kritik und Verbesserungsvor schläge dankbar. Klausdorf, im Herbst 1983 Lothar Sachs Aus dem Vorwort zur vierten Diese Neufassung mit angemessenerem Titel ist zugleich ein zum Lesen und Lernen geschriebenes einführendes und weiterführendes Lehrbuch und ein Nachschlagewerk mit Formelsammlung, Tabellensammlung, zahlreichen Querverbindungen aufzeigen den Seitenverweisen, ausführlicher Bibliographie, Namenverzeichnis und ausführli chem Sachverzeichnis. Sie enthält wieder eine Fülle von Verbesserungen, vor allem Vereinfachungen und Präzisierungen. Große Teile des Textes und der Literatur habe ich den neuen Erkenntnissen entsprechend überarbeitet, durch erweiterte Neufassun gen ersetzt oder eingefügt; dies gilt auch für den Tabellenteil (Übersicht gegenüber dem Titelblatt; S. 34, 53, 112, 127, 147, 172, 198,220,225,240,256,272,424,425, Rückseite der vorletzten Seite). Vielen kritischen Freunden des Buches-insbesondere Ingenieuren-sei für Anregungen gedankt, die beiden Büchern zugute gekommen sind.Combinatorial analysis

Author: V. Sidoravicius,S. Smirnov

Publisher: American Mathematical Soc.

ISBN: 1470422484

Category: Combinatorial analysis

Page: 471

View: 4373

This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.Mathematics

Author: William Feller

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 528

View: 2374

The nature of probability theory. The sample space. Elements of combinatorial analysis. Fluctuations in coin tossing and random walks. Combination of events. Conditional probability, stochastic independence. The binomial and the Poisson distributions. The Normal approximation to the binomial distribution. Unlimited sequences of Bernoulli trials. Random variables, expectation. Laws of large numbers. Integral valued variables, generating functions. Compound distributions. Branching processes. Recurrent events. Renewal theory. Random walk and ruin problems. Markov chains. Algebraic treatment of finite Markov chains. The simplest time-dependent stochastic processes. Answer to problems. Index.Business & Economics

*Key Concepts and Problems*

Author: K. Patterson

Publisher: Springer

ISBN: 023029930X

Category: Business & Economics

Page: 641

View: 7660

Testing for a unit root is now an essential part of time series analysis. This volume provides a critical overview and assessment of tests for a unit root in time series, developing the concepts necessary to understand the key theoretical and practical models in unit root testing.Business & Economics

*Basic Ideas and Selected Topics, Volume I, Second Edition*

Author: Peter J. Bickel,Kjell A. Doksum

Publisher: CRC Press

ISBN: 1498723810

Category: Business & Economics

Page: 576

View: 8037

Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition presents fundamental, classical statistical concepts at the doctorate level. It covers estimation, prediction, testing, confidence sets, Bayesian analysis, and the general approach of decision theory. This edition gives careful proofs of major results and explains how the theory sheds light on the properties of practical methods. The book first discusses non- and semiparametric models before covering parameters and parametric models. It then offers a detailed treatment of maximum likelihood estimates (MLEs) and examines the theory of testing and confidence regions, including optimality theory for estimation and elementary robustness considerations. It next presents basic asymptotic approximations with one-dimensional parameter models as examples. The book also describes inference in multivariate (multiparameter) models, exploring asymptotic normality and optimality of MLEs, Wald and Rao statistics, generalized linear models, and more. Mathematical Statistics: Basic Ideas and Selected Topics, Volume II will be published in 2015. It will present important statistical concepts, methods, and tools not covered in Volume I.Mathematics

Author: Alexandr A. Borovkov

Publisher: Springer Science & Business Media

ISBN: 1447152018

Category: Mathematics

Page: 733

View: 5253

This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent. The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects. Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study.Mathematics

*Parts 1 and 2*

Author: I͡U. N. Linʹkov

Publisher: American Mathematical Soc.

ISBN: 9780821889688

Category: Mathematics

Page: 321

View: 6069

This volume is intended for the advanced study of several topics in mathematical statistics. The first part of the book is devoted to sampling theory (from one-dimensional and multidimensional distributions), asymptotic properties of sampling, parameter estimation, sufficient statistics, and statistical estimates. The second part is devoted to hypothesis testing and includes the discussion of families of statistical hypotheses that can be asymptotically distinguished. In particular,the author describes goodness-of-fit and sequential statistical criteria (Kolmogorov, Pearson, Smirnov, and Wald) and studies their main properties. The book is suitable for graduate students and researchers interested in mathematical statistics. It is useful for independent study or supplementaryreading.Technology & Engineering

Author: Edwin F. Beckenbach

Publisher: Courier Corporation

ISBN: 0486316122

Category: Technology & Engineering

Page: 480

View: 8135

The second in this two-volume series also contains original papers commissioned from prominent 20th-century mathematicians. A three-part treatment covers mathematical methods, statistical and scheduling studies, and physical phenomena. 1961 edition.Mathematics

*High-Dimensional and Large-Sample Approximations*

Author: Yasunori Fujikoshi,Vladimir V. Ulyanov,Ryoichi Shimizu

Publisher: John Wiley & Sons

ISBN: 0470411694

Category: Mathematics

Page: 533

View: 1454

A comprehensive examination of high-dimensional analysis ofmultivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-SampleApproximations is the first book of its kind to explore howclassical multivariate methods can be revised and used in place ofconventional statistical tools. Written by prominent researchers inthe field, the book focuses on high-dimensional and large-scaleapproximations and details the many basic multivariate methods usedto achieve high levels of accuracy. The authors begin with a fundamental presentation of the basictools and exact distributional results of multivariate statistics,and, in addition, the derivations of most distributional resultsare provided. Statistical methods for high-dimensional data, suchas curve data, spectra, images, and DNA microarrays, are discussed.Bootstrap approximations from a methodological point of view,theoretical accuracies in MANOVA tests, and model selectioncriteria are also presented. Subsequent chapters feature additionaltopical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance indiscriminant analysis, growth curve models, generalized linearmodels, profile analysis, and multiple comparison Each chapter provides real-world applications and thoroughanalyses of the real data. In addition, approximation formulasfound throughout the book are a useful tool for both practical andtheoretical statisticians, and basic results on exact distributionsin multivariate analysis are included in a comprehensive, yetaccessible, format. Multivariate Statistics is an excellent book for courseson probability theory in statistics at the graduate level. It isalso an essential reference for both practical and theoreticalstatisticians who are interested in multivariate analysis and whowould benefit from learning the applications of analyticalprobabilistic methods in statistics.Mathematics

Author: Fazlollah M. Reza

Publisher: Courier Corporation

ISBN: 0486158446

Category: Mathematics

Page: 528

View: 5274

Graduate-level study for engineering students presents elements of modern probability theory, information theory, coding theory, more. Emphasis on sample space, random variables, capacity, etc. Many reference tables and extensive bibliography. 1961 edition.Probabilities

Author: Alʹbert Nikolaevich Shiri︠a︡ev,Hans Jürgen Engelbert

Publisher: N.A

ISBN: N.A

Category: Probabilities

Page: 592

View: 7411

Mathematics

Author: Yuriy Kharin

Publisher: Springer Science & Business Media

ISBN: 3319008404

Category: Mathematics

Page: 356

View: 8259

This book offers solutions to such topical problems as developing mathematical models and descriptions of typical distortions in applied forecasting problems; evaluating robustness for traditional forecasting procedures under distortionism and more.Education

*Statistical Detection and Methodology*

Author: Neal Kingston,Amy Clark

Publisher: Routledge

ISBN: 1134650671

Category: Education

Page: 268

View: 1270

There has been an increase in awareness (and perhaps occurrence) of individual and organized cheating on tests. Recent reports of widespread problems with state student accountability tests and teacher certification testing have raised questions about the very validity of assessment programs. While there are several books that specifically detail the issues of test security cheating on assessments, few outline the statistical procedures used for detecting various types of potential test fraud and the associated research findings. Without a significant research literature base, the new generation of researchers will have little opportunity or incentive to improve on existing methods. Enlisting a variety of experts and scholars in different fields of testing, this edited volume expands on the current literature base by including examples of detailed research findings arrived at by statistical methodology. It also provides a synthesis of the current state of the art with regard to the statistical detection of testing infidelity, particularly for large-scale assessments. By presenting methods currently used by testing organizations and research on new methods, the volume offers an important forum for expanding the literature in this area.Mathematics

Author: John Geweke

Publisher: John Wiley & Sons

ISBN: 0471744727

Category: Mathematics

Page: 300

View: 9831

Tools to improve decision making in an imperfect world This publication provides readers with a thorough understanding ofBayesian analysis that is grounded in the theory of inference andoptimal decision making. Contemporary Bayesian Econometrics andStatistics provides readers with state-of-the-art simulationmethods and models that are used to solve complex real-worldproblems. Armed with a strong foundation in both theory andpractical problem-solving tools, readers discover how to optimizedecision making when faced with problems that involve limited orimperfect data. The book begins by examining the theoretical and mathematicalfoundations of Bayesian statistics to help readers understand howand why it is used in problem solving. The author then describeshow modern simulation methods make Bayesian approaches practicalusing widely available mathematical applications software. Inaddition, the author details how models can be applied to specificproblems, including: * Linear models and policy choices * Modeling with latent variables and missing data * Time series models and prediction * Comparison and evaluation of models The publication has been developed and fine- tuned through a decadeof classroom experience, and readers will find the author'sapproach very engaging and accessible. There are nearly 200examples and exercises to help readers see how effective use ofBayesian statistics enables them to make optimal decisions. MATLAB?and R computer programs are integrated throughout the book. Anaccompanying Web site provides readers with computer code for manyexamples and datasets. This publication is tailored for research professionals who useeconometrics and similar statistical methods in their work. Withits emphasis on practical problem solving and extensive use ofexamples and exercises, this is also an excellent textbook forgraduate-level students in a broad range of fields, includingeconomics, statistics, the social sciences, business, and publicpolicy.Library catalogs

Mathematics

Author: Patrick Billingsley

Publisher: John Wiley & Sons

ISBN: 1118341910

Category: Mathematics

Page: 656

View: 6023

Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style. In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students. This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book. The Anniversary Edition contains features including: An improved treatment of Brownian motion Replacement of queuing theory with ergodic theory Theory and applications used to illustrate real-life situations Over 300 problems with corresponding, intensive notes and solutions Updated bibliography An extensive supplement of additional notes on the problems and chapter commentaries Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011. Billingsley earned his Bachelor's Degree in Engineering from the U.S. Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R. Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics. This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.Mathematics

*An Introduction*

Author: Timo Koski,John Noble

Publisher: John Wiley & Sons

ISBN: 1119964954

Category: Mathematics

Page: 366

View: 3203

Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include: An introduction to Dirichlet Distribution, Exponential Families and their applications. A detailed description of learning algorithms and Conditional Gaussian Distributions using Junction Tree methods. A discussion of Pearl's intervention calculus, with an introduction to the notion of see and do conditioning. All concepts are clearly defined and illustrated with examples and exercises. Solutions are provided online. This book will prove a valuable resource for postgraduate students of statistics, computer engineering, mathematics, data mining, artificial intelligence, and biology. Researchers and users of comparable modelling or statistical techniques such as neural networks will also find this book of interest.Mathematics

Author: X. Sheldon Lin,Society of Actuaries

Publisher: John Wiley & Sons

ISBN: 0471793205

Category: Mathematics

Page: 224

View: 8939

Incorporates the many tools needed for modeling and pricing infinance and insurance Introductory Stochastic Analysis for Finance and Insuranceintroduces readers to the topics needed to master and use basicstochastic analysis techniques for mathematical finance. The authorpresents the theories of stochastic processes and stochasticcalculus and provides the necessary tools for modeling and pricingin finance and insurance. Practical in focus, the book's emphasisis on application, intuition, and computation, rather thantheory. Consequently, the text is of interest to graduate students,researchers, and practitioners interested in these areas. While thetext is self-contained, an introductory course in probabilitytheory is beneficial to prospective readers. This book evolved from the author's experience as an instructor andhas been thoroughly classroom-tested. Following an introduction,the author sets forth the fundamental information and tools neededby researchers and practitioners working in the financial andinsurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics andApplications in Insurance, are devoted to more advanced topics.Readers learn the Feynman-Kac formula, the Girsanov's theorem, andcomplex barrier hitting times distributions. Finally, readersdiscover how stochastic analysis and principles are applied inpractice through two insurance examples: valuation of equity-linkedannuities under a stochastic interest rate environment andcalculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplifycomplex theory and pro-cesses. An extensive bibliography opens upadditional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, thistext is recommended for one-semester courses in stochastic financeand calculus. It is also recommended as a study guide forprofessionals taking Causality Actuarial Society (CAS) and Societyof Actuaries (SOA) actuarial examinations.