Number Theoretic Methods In Statistics
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Number Theoretic Methods In Statistics
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Author : Kai-Tai Fang
language : en
Publisher: CRC Press
Release Date : 1993-12-01
Number Theoretic Methods In Statistics written by Kai-Tai Fang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-01 with Mathematics categories.
This book is a survey of recent work on the application of number theory in statistics. The essence of number-theoretic methods is to find a set of points that are universally scattered over an s-dimensional unit cube. In certain circumstances this set can be used instead of random numbers in the Monte Carlo method. The idea can also be applied to other problems such as in experimental design. This book will illustrate the idea of number-theoretic methods and their application in statistics. The emphasis is on applying the methods to practical problems so only part-proofs of theorems are given.
Number Theoretic Methods In Statistics
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Author : Kai-tai Fang
language : en
Publisher: Springer
Release Date : 2013-11-07
Number Theoretic Methods In Statistics written by Kai-tai Fang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-07 with Mathematics categories.
This book contains some of the research work conducted by the authors in past seventeen years. Our research started in 1976. At that time, the first author was studying a problem of alloy steel standardization, where aseries of probabilities of the 5-dimensional normal distribution needed to be calculated. Since the usual meth ods for numerical evaluation of multiple definite integral were all ineffective, he asked the second author for input on the number theoretic method for numerical integration. As a result, his prob lem was solved by using the number-theoretic method. The essence of the number-theoretic method (NTM) is to find a set of points that is uniformly scattered over an s-dimensional unit cube, and sometimes this set can be used instead of random number in Monte Carlo method. The authors then understood that this idea can apply also to some other problems, for instance, problems in ex perimental design. In 1978, a Chinese industrial agency proposed a problem of ex perimental designs to the authors, where six factors with at least 12 levels for each factors should be considered. Since the experiment was quite expensive, we were asked to provide an efficient exper imental design within 50 experiments. This lead us to study the problem on how to apply the number-theoretic method to arrange the experiments, and we proposed a so-called "uniform design" for designing experiments.
Numerical Methods Of Statistics
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Author : John F. Monahan
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-05
Numerical Methods Of Statistics written by John F. Monahan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-05 with Computers categories.
This 2001 book provides a basic background in numerical analysis and its applications in statistics.
Theoretical Statistics
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Author : Robert W. Keener
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-08
Theoretical Statistics written by Robert W. Keener and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-08 with Mathematics categories.
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.
Set Theoretic Methods In Control
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Author : Franco Blanchini
language : en
Publisher: Birkhäuser
Release Date : 2015-07-02
Set Theoretic Methods In Control written by Franco Blanchini and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-02 with Science categories.
The second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint. This approach is linked to fundamental control problems, such as Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. Completely self-contained, this book provides a solid foundation of mathematical techniques and applications, extensive references to the relevant literature, and numerous avenues for further theoretical study. All the material from the first edition has been updated to reflect the most recent developments in the field, and a new chapter on switching systems has been added. Each chapter contains examples, case studies, and exercises to allow for a better understanding of theoretical concepts by practical application. The mathematical language is kept to the minimum level necessary for the adequate formulation and statement of the main concepts, yet allowing for a detailed exposition of the numerical algorithms for the solution of the proposed problems. Set-Theoretic Methods in Control will appeal to both researchers and practitioners in control engineering and applied mathematics. It is also well-suited as a textbook for graduate students in these areas. Praise for the First Edition "This is an excellent book, full of new ideas and collecting a lot of diverse material related to set-theoretic methods. It can be recommended to a wide control community audience." - B. T. Polyak, Mathematical Reviews "This book is an outstanding monograph of a recent research trend in control. It reflects the vast experience of the authors as well as their noticeable contributions to the development of this field...[It] is highly recommended to PhD students and researchers working in control engineering or applied mathematics. The material can also be used for graduate courses in these areas." - Octavian Pastravanu, Zentralblatt MATH
Statistical Methods
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Author : Donna L. Mohr
language : en
Publisher: Academic Press
Release Date : 2010-08-17
Statistical Methods written by Donna L. Mohr and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-17 with Mathematics categories.
Statistical Methods, Third Edition, provides students with a working introduction to statistical methods offering a wide range of applications that emphasize the quantitative skills useful across many academic disciplines. This text takes a classic approach that emphasizes concepts and techniques for working out problems and intepreting results. The book includes research projects, real-world case studies, numerous examples, and data exercises organized by level of difficulty. Students are required to be familiar with algebra. This updated edition includes new exercises applying different techniques and methods; new examples and datasets using current real-world data; new text organization to create a more natural connection between regression and the Analysis of the Variance; new material on generalized linear models; new expansion of nonparametric techniques; new student research projects; and new case studies for gathering, summarizing, and analyzing data. - Integrates the classical conceptual approach with modern day computerized data manipulation and computer applications - Accessibile to students who may not have a background in probability or calculus - Offers reader-friendly exposition, without sacrificing statistical rigor - Includes many new data sets in various applied fields such as Psychology, Education, Biostatistics, Agriculture, Economics
Theory And Methods Of Statistics
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Author : P.K. Bhattacharya
language : en
Publisher: Academic Press
Release Date : 2016-05-27
Theory And Methods Of Statistics written by P.K. Bhattacharya and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-27 with Mathematics categories.
Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures.
A Course In Mathematical Statistics And Large Sample Theory
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Author : Rabi Bhattacharya
language : en
Publisher: Springer
Release Date : 2016-08-13
A Course In Mathematical Statistics And Large Sample Theory written by Rabi Bhattacharya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-13 with Mathematics categories.
This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.
All Of Statistics
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Author : Larry Wasserman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
All Of Statistics written by Larry Wasserman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Selected Papers Of Wang Yuan
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Author : Yuan Wang
language : en
Publisher: World Scientific
Release Date : 2005
Selected Papers Of Wang Yuan written by Yuan Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume presents a comprehensive collection of Wang Yuan's original important papers which are not available elsewhere, since the majority of the papers were published in China.Covering both pure number theory and applied mathematics, this book is important for understanding Wang Yuan's academic career and also the development of Chinese mathematics in recent years, since Wang Yuan's work has a wide-ranging influence in China.Wang Yuan is a professor and academician of the Chinese Academy of Sciences. He received his honorable Doctorship from Hong Kong Baptist University. He has published 70 papers and ten books.