Statistical Implications Of Turing S Formula
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Statistical Implications Of Turing S Formula
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Author : Zhiyi Zhang
language : en
Publisher: John Wiley & Sons
Release Date : 2016-11-21
Statistical Implications Of Turing S Formula written by Zhiyi Zhang and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-21 with Mathematics categories.
Features a broad introduction to recent research on Turing’s formula and presents modern applications in statistics, probability, information theory, and other areas of modern data science Turing's formula is, perhaps, the only known method for estimating the underlying distributional characteristics beyond the range of observed data without making any parametric or semiparametric assumptions. This book presents a clear introduction to Turing’s formula and its connections to statistics. Topics with relevance to a variety of different fields of study are included such as information theory; statistics; probability; computer science inclusive of artificial intelligence and machine learning; big data; biology; ecology; and genetics. The author provides examinations of many core statistical issues within modern data science from Turing's perspective. A systematic approach to long-standing problems such as entropy and mutual information estimation, diversity index estimation, domains of attraction on general alphabets, and tail probability estimation is presented in light of the most up-to-date understanding of Turing's formula. Featuring numerous exercises and examples throughout, the author provides a summary of the known properties of Turing's formula and explains how and when it works well; discusses the approach derived from Turing's formula in order to estimate a variety of quantities, all of which mainly come from information theory, but are also important for machine learning and for ecological applications; and uses Turing's formula to estimate certain heavy-tailed distributions. In summary, this book: • Features a unified and broad presentation of Turing’s formula, including its connections to statistics, probability, information theory, and other areas of modern data science • Provides a presentation on the statistical estimation of information theoretic quantities • Demonstrates the estimation problems of several statistical functions from Turing's perspective such as Simpson's indices, Shannon's entropy, general diversity indices, mutual information, and Kullback–Leibler divergence • Includes numerous exercises and examples throughout with a fundamental perspective on the key results of Turing’s formula Statistical Implications of Turing's Formula is an ideal reference for researchers and practitioners who need a review of the many critical statistical issues of modern data science. This book is also an appropriate learning resource for biologists, ecologists, and geneticists who are involved with the concept of diversity and its estimation and can be used as a textbook for graduate courses in mathematics, probability, statistics, computer science, artificial intelligence, machine learning, big data, and information theory. Zhiyi Zhang, PhD, is Professor of Mathematics and Statistics at The University of North Carolina at Charlotte. He is an active consultant in both industry and government on a wide range of statistical issues, and his current research interests include Turing's formula and its statistical implications; probability and statistics on countable alphabets; nonparametric estimation of entropy and mutual information; tail probability and biodiversity indices; and applications involving extracting statistical information from low-frequency data space. He earned his PhD in Statistics from Rutgers University.
A Normal Country
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Author : Andrei Shleifer
language : en
Publisher: Harvard University Press
Release Date : 2005
A Normal Country written by Andrei Shleifer and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Business & Economics categories.
This book offers a firsthand glimpse into the intellectual challenges that Russia's turbulent transition generated. It deals with many of the most important reforms, from Gorbachev's half-hearted "perestroika," to the mass privatization program, to the efforts to build legal and regulatory institutions of a market economy.
Theory Of Statistical Inference
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Author : Anthony Almudevar
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Theory Of Statistical Inference written by Anthony Almudevar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.
Statistical Design And Analysis In Pharmaceutical Science
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Author : Shein-Chung Chow
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Statistical Design And Analysis In Pharmaceutical Science written by Shein-Chung Chow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
"Offers a comprehensive, unified presentation of statistical designs and methods of analysis for all stages of pharmaceutical development--emphasizing biopharmaceutical applications and demonstrating statistical techniques with real-world examples."
Guide To Programs
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Author : National Science Foundation (U.S.)
language : en
Publisher:
Release Date : 1994
Guide To Programs written by National Science Foundation (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
The Role Of Major Nonfuel Minerals In The Asian Pacific Rim Economies
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Author : Julius C. Chang
language : en
Publisher:
Release Date : 1993
The Role Of Major Nonfuel Minerals In The Asian Pacific Rim Economies written by Julius C. Chang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Nonfuel mineral industries categories.
Permutation Statistical Methods
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Author : Kenneth J. Berry
language : en
Publisher: Springer
Release Date : 2016-05-03
Permutation Statistical Methods written by Kenneth J. Berry and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-03 with Mathematics categories.
This research monograph provides a synthesis of a number of statistical tests and measures, which, at first consideration, appear disjoint and unrelated. Numerous comparisons of permutation and classical statistical methods are presented, and the two methods are compared via probability values and, where appropriate, measures of effect size. Permutation statistical methods, compared to classical statistical methods, do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This text takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field in statistics. This topic is new in that it took modern computing power to make permutation methods available to people working in the mainstream of research. lly-informed="" audience,="" and="" can="" also="" easily="" serve="" as="" textbook="" in="" graduate="" course="" departments="" such="" statistics,="" psychology,="" or="" biology.="" particular,="" the="" audience="" for="" book="" is="" teachers="" of="" practicing="" statisticians,="" applied="" quantitative="" students="" fields="" medical="" research,="" epidemiology,="" public="" health,="" biology.
Oecd Employment Outlook 1997 July
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Author : OECD
language : en
Publisher: OECD Publishing
Release Date : 1997-07-09
Oecd Employment Outlook 1997 July written by OECD and has been published by OECD Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-09 with categories.
The OECD Employment Outlook provides an annual assessment of labour market developments and prospects in Member countries. Each issue contains an overall analysis of the latest market trends and short-term forecasts, and examines key labour market developments. Reference statistics are included.
The Review Of Economics And Statistics
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Author :
language : en
Publisher:
Release Date : 1958
The Review Of Economics And Statistics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Computer network resources categories.
The purpose of the Review is to promote the collection, criticism, and interpretation of economic statistics, with a view to making them more accurate and valuable than they are at present for business and scientific purposes.
Encyclopedia Of Software Engineering Three Volume Set Print
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Author : Phillip A. Laplante
language : en
Publisher: CRC Press
Release Date : 2010-11-22
Encyclopedia Of Software Engineering Three Volume Set Print written by Phillip A. Laplante and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-22 with Computers categories.
Software engineering requires specialized knowledge of a broad spectrum of topics, including the construction of software and the platforms, applications, and environments in which the software operates as well as an understanding of the people who build and use the software. Offering an authoritative perspective, the two volumes of the Encyclopedia of Software Engineering cover the entire multidisciplinary scope of this important field. More than 200 expert contributors and reviewers from industry and academia across 21 countries provide easy-to-read entries that cover software requirements, design, construction, testing, maintenance, configuration management, quality control, and software engineering management tools and methods. Editor Phillip A. Laplante uses the most universally recognized definition of the areas of relevance to software engineering, the Software Engineering Body of Knowledge (SWEBOK®), as a template for organizing the material. Also available in an electronic format, this encyclopedia supplies software engineering students, IT professionals, researchers, managers, and scholars with unrivaled coverage of the topics that encompass this ever-changing field. Also Available Online This Taylor & Francis encyclopedia is also available through online subscription, offering a variety of extra benefits for researchers, students, and librarians, including: Citation tracking and alerts Active reference linking Saved searches and marked lists HTML and PDF format options Contact Taylor and Francis for more information or to inquire about subscription options and print/online combination packages. US: (Tel) 1.888.318.2367; (E-mail) [email protected] International: (Tel) +44 (0) 20 7017 6062; (E-mail) [email protected]