Introduction to Statistical Limit Theory PDF Download
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Author: Alan M. Polansky
Publisher: CRC Press
ISBN: 1420076612
Category : Mathematics
Languages : en
Pages : 645
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Book Description
Helping students develop a good understanding of asymptotic theory, Introduction to Statistical Limit Theory provides a thorough yet accessible treatment of common modes of convergence and their related tools used in statistics. It also discusses how the results can be applied to several common areas in the field.The author explains as much of the
Author: Alan M. Polansky
Publisher: CRC Press
ISBN: 1420076612
Category : Mathematics
Languages : en
Pages : 645
Get Book
Book Description
Helping students develop a good understanding of asymptotic theory, Introduction to Statistical Limit Theory provides a thorough yet accessible treatment of common modes of convergence and their related tools used in statistics. It also discusses how the results can be applied to several common areas in the field.The author explains as much of the
Author: Barbara Illowsky
Publisher:
ISBN: 9781998295470
Category : Business & Economics
Languages : en
Pages : 0
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Book Description
Book Publication Date: Dec 13, 2023. Full color. Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills.
Author: I. Berkes
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 572
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Book Description
Author: Victor H. Peña
Publisher: Springer Science & Business Media
ISBN: 3540856366
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.
Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
ISBN: 9401735158
Category : Mathematics
Languages : en
Pages : 558
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Book Description
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
Author: David Diez
Publisher:
ISBN: 9781943450046
Category :
Languages : en
Pages :
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Book Description
The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources.
Author: James H. Stapleton
Publisher: John Wiley & Sons
ISBN: 0470183403
Category : Mathematics
Languages : en
Pages : 466
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Book Description
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.
Author: Hans Fischer
Publisher: Springer Science & Business Media
ISBN: 0387878572
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Author: Arnold I. Davidson
Publisher: Oxford University Press
ISBN: 0198774036
Category : Business & Economics
Languages : en
Pages : 562
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Book Description
This major new econometrics text surveys recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity. Designed for econometricians and advanced students with limited mathematical training, the book clearly lays out the necessary math and probability theory and uses numerous examples to make its data useful and comprehensible. It also includes original new material from Davidson's own research on central limit theorems. About the Series Advanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.
Author: I︠A︡kov Grigorʹevich Sinaĭ
Publisher: Springer Science & Business Media
ISBN: 9783540533481
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book is an excellent introduction to probability theory for students who have some general experience from university-level mathematics, in particular, analysis. It would be suitable for reading in conjunction with a second or third year course in probability theory. Besides the standard material, the author has included sections on special topics, for example percolation and statistical mechanics, which are direct applications of the theory.
