Mathematical Theory Of Statistics

Author : Helmut Strasser
Publisher : Walter de Gruyter
Page : 505 pages
File Size : 52,8 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110850826

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Mathematical Theory of Statistics by Helmut Strasser Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Author : Richard von Mises
Publisher : Academic Press
Page : 708 pages
File Size : 53,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483264028

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Mathematical Theory of Probability and Statistics by Richard von Mises Pdf

Mathematical Theory of Probability and Statistics focuses on the contributions and influence of Richard von Mises on the processes, methodologies, and approaches involved in the mathematical theory of probability and statistics. The publication first elaborates on fundamentals, general label space, and basic properties of distributions. Discussions focus on Gaussian distribution, Poisson distribution, mean value variance and other moments, non-countable label space, basic assumptions, operations, and distribution function. The text then ponders on examples of combined operations and summation of chance variables characteristic function. The book takes a look at the asymptotic distribution of the sum of chance variables and probability inference. Topics include inference from a finite number of observations, law of large numbers, asymptotic distributions, limit distribution of the sum of independent discrete random variables, probability of the sum of rare events, and probability density. The text also focuses on the introduction to the theory of statistical functions and multivariate statistics. The publication is a dependable source of information for researchers interested in the mathematical theory of probability and statistics

Author : Robert V. Hogg,Allen Thornton Craig
Publisher : Unknown
Page : 88 pages
File Size : 40,9 Mb
Release : 1995
Category : Mathematical statistics
ISBN : 0132089351

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Introduction to Mathematical Statistics, Fifth Edition by Robert V. Hogg,Allen Thornton Craig Pdf

Author : Sumio Watanabe
Publisher : CRC Press
Page : 320 pages
File Size : 53,5 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781482238082

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Mathematical Theory of Bayesian Statistics by Sumio Watanabe Pdf

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

Author : David A. Blackwell,M. A. Girshick
Publisher : Courier Corporation
Page : 388 pages
File Size : 44,9 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780486150895

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Theory of Games and Statistical Decisions by David A. Blackwell,M. A. Girshick Pdf

Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.

Author : Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru
Publisher : Springer
Page : 389 pages
File Size : 42,6 Mb
Release : 2016-08-13
Category : Mathematics
ISBN : 9781493940325

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A Course in Mathematical Statistics and Large Sample Theory by Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru Pdf

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.

Author : Vladimir S. Korolyuk,Y.V. Borovskich
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401735155

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Theory of U-Statistics by Vladimir S. Korolyuk,Y.V. Borovskich Pdf

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 : Harald Cramér
Publisher : Unknown
Page : 575 pages
File Size : 51,8 Mb
Release : 1946
Category : Mathematical statistics
ISBN : OCLC:185899566

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Mathematical Methods of Statistics by Harald Cramér Pdf

Author : A. A. Sveshnikov
Publisher : Courier Corporation
Page : 512 pages
File Size : 46,7 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486137568

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Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions by A. A. Sveshnikov Pdf

Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

Author : Dieter Rasch,Dieter Schott
Publisher : John Wiley & Sons
Page : 886 pages
File Size : 51,6 Mb
Release : 2018-01-09
Category : Mathematics
ISBN : 9781119385233

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Mathematical Statistics by Dieter Rasch,Dieter Schott Pdf

Explores mathematical statistics in its entirety—from the fundamentals to modern methods This book introduces readers to point estimation, confidence intervals, and statistical tests. Based on the general theory of linear models, it provides an in-depth overview of the following: analysis of variance (ANOVA) for models with fixed, random, and mixed effects; regression analysis is also first presented for linear models with fixed, random, and mixed effects before being expanded to nonlinear models; statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests; and design of experiments from a mathematical-statistical point of view. Most analysis methods have been supplemented by formulae for minimal sample sizes. The chapters also contain exercises with hints for solutions. Translated from the successful German text, Mathematical Statistics requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables), which is typically taught in the earlier semesters of scientific and mathematical study courses. It teaches readers all about statistical analysis and covers the design of experiments. The book also describes optimal allocation in the chapters on regression analysis. Additionally, it features a chapter devoted solely to experimental designs. Classroom-tested with exercises included Practice-oriented (taken from day-to-day statistical work of the authors) Includes further studies including design of experiments and sample sizing Presents and uses IBM SPSS Statistics 24 for practical calculations of data Mathematical Statistics is a recommended text for advanced students and practitioners of math, probability, and statistics.

Author : S. S. Wilks
Publisher : Read Books Ltd
Page : 404 pages
File Size : 44,7 Mb
Release : 2012-11-19
Category : Mathematics
ISBN : 9781447496748

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Mathematical Statistics by S. S. Wilks Pdf

This book contains S. S. Wilks' lessons on mathematical statistics, and will make an excellent addition to the bookshelf of anyone with an interest in the subject. Preface: 'Most of the mathematical theory of statistics in its present state has been developed during the past twenty years. Because of the variety of scientific fields in which statistical problems have arisen, the original contributions to this branch of applied mathematics are widely scattered in scientific literature. Most of the theory still exists only in original form. During the past few years the author has conducted a two-semester course at Princeton University for advanced undergraduates and beginning graduate students in which an attempt has been made to give the students an introduction to the more recent developments in the mathematical theory of statistics. The subject matter for this course has been gleaned, for the most part, from periodical literature. Since it is impossible to cover in detail any large portion of this literature in two semesters, the course has been held primarily to the basic mathematics of the material, with just enough problems and examples for illustrative and examination purposes...'

Author : Johann Pfanzagl
Publisher : Springer
Page : 316 pages
File Size : 54,9 Mb
Release : 2017-10-23
Category : Mathematics
ISBN : 9783642310843

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Mathematical Statistics by Johann Pfanzagl Pdf

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

Author : Hilda Geiringer
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 1964
Category : Electronic
ISBN : OCLC:1048645112

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Mathematical Theory of Probability and by Hilda Geiringer Pdf

Author : Victor M. Panaretos
Publisher : Birkhäuser
Page : 177 pages
File Size : 42,7 Mb
Release : 2016-06-01
Category : Mathematics
ISBN : 9783319283418

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Statistics for Mathematicians by Victor M. Panaretos Pdf

This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students.

Author : Aleksandr Petrovich Korostelev,Olga Korosteleva
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 44,6 Mb
Release : 2011
Category : Asymptotic efficiencies (Statistics).
ISBN : 9780821852835

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Mathematical Statistics by Aleksandr Petrovich Korostelev,Olga Korosteleva Pdf

iPositive Give a man a fish, he eats for a day, but if you teach him to fish, you feed him for life. Such is the approach of iPositive. One day at the gym doesnt make a person fit for life; its a consistent dedication to getting the body in shape that eventually yields results. The lessons in iPositive work in much the same way: They challenge the reader to work to keep the mind in shape. The book is a powerful guide to personal happiness through positivity. Its concepts provide empowerment to overcome self-doubt, disbelief and inferiority complexes in order to transcend the negativity in life. iPositive is geared toward helping individuals become more focused on the things they most want in life, like happiness, love and success, or banish anchors that may be weighting them down, like stress, smoking or excess weight. The book gives readers the practical means to become more focused on those things they want in life, and serves as an inspirational manual for a life of fulfillment, and strength in body, mind and spirit.