basics of modern mathematical statistics springer texts in statistics

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Basics Of Modern Mathematical Statistics

Author : Vladimir Spokoiny
ISBN : 9783642399091
Genre : Mathematics
File Size : 78. 50 MB
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This textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious study or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics. This textbook is primarily intended for graduate and postdoc students and young researchers who are interested in modern statistical methods.

Modern Mathematical Statistics With Applications

Author : Jay L. Devore
ISBN : 9781461403906
Genre : Mathematics
File Size : 29. 25 MB
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Many mathematical statistics texts are heavily oriented toward a rigorous mathematical development of probability and statistics, without much attention paid to how statistics is actually used.. In contrast, Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data. The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research. It begins with a chapter on descriptive statistics that immediately exposes the reader to real data. The next six chapters develop the probability material that bridges the gap between descriptive and inferential statistics. Point estimation, inferences based on statistical intervals, and hypothesis testing are then introduced in the next three chapters. The remainder of the book explores the use of this methodology in a variety of more complex settings. This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics. Representative applications include investigating whether the average tip percentage in a particular restaurant exceeds the standard 15%, considering whether the flavor and aroma of Champagne are affected by bottle temperature or type of pour, modeling the relationship between college graduation rate and average SAT score, and assessing the likelihood of O-ring failure in space shuttle launches as related to launch temperature.

All Of Statistics

Author : Larry Wasserman
ISBN : 9780387217369
Genre : Mathematics
File Size : 53. 64 MB
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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.

A Modern Introduction To Probability And Statistics

Author : F.M. Dekking
ISBN : 9781846281686
Genre : Mathematics
File Size : 54. 65 MB
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Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

Mathematical Statistics

Author : Jun Shao
ISBN : 9780387953823
Genre : Mathematics
File Size : 25. 31 MB
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This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are usefulin statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to the classical results that are typically covered in a textbook of a similar level, this book introduces some topics in modern statistical theory that have been developed in recent years, such as Markov chain Monte Carlo, quasi-likelihoods, empirical likelihoods, statistical functionals, generalized estimation equations, the jackknife, and the bootstrap. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison. Also available: Jun Shao and Dongsheng Tu, The Jackknife and Bootstrap, Springer- Verlag New York, Inc., 1995, Cloth, 536 pp., 0-387-94515-6.

Mathematical Statistics

Author : George R. Terrell
ISBN : 9780387986210
Genre : Mathematics
File Size : 25. 55 MB
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This textbook introduces the mathematical concepts & methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed, being developed as needed. The book is committed to both a high level of mathematical seriousness & to an intimate connection with application. The text is aimed at the upper undergraduate or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra & infinite series.

Mathematical Statistics

Author : Dieter Rasch
ISBN : 9781119385288
Genre : Mathematics
File Size : 66. 62 MB
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This book 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. After the basic ideas of mathematical statistics, Mathematical Statistics gives an introduction to point estimation, confidence intervals and statistical tests. Based on the general theory of linear models, the book provides an in-depth overview of the following: Analysis of variance 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 Design of experiments from a mathematical-statistical point of view. The chapters also contain exercises with hints for solutions.

Fundamentals Of Statistics With Fuzzy Data

Author : Hung T. Nguyen
ISBN : 3540819983
Genre : Mathematics
File Size : 69. 97 MB
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This book presents basic aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The book aims at motivating statisticians to examine fuzzy statistics to enlarge the domain of applicability of statistics in general.

Theoretical Statistics

Author : Robert W. Keener
ISBN : 0387938397
Genre : Mathematics
File Size : 31. 29 MB
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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.

An Introduction To Statistical Learning

Author : Gareth James
ISBN : 9781461471387
Genre : Mathematics
File Size : 32. 15 MB
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An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

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