Theoretical Statistics
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Author | : Robert W. Keener |
Publisher | : Springer Science & Business Media |
Total Pages | : 543 |
Release | : 2010-09-08 |
Genre | : Mathematics |
ISBN | : 0387938397 |
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.
Author | : D.R. Cox |
Publisher | : CRC Press |
Total Pages | : 1060 |
Release | : 1979-09-06 |
Genre | : Mathematics |
ISBN | : 9780412161605 |
A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistical procedures. Chapters 4 and 5 cover hypothesis testing with simple and null hypotheses, respectively. Subsequent chapters discuss non-parametrics, interval estimation, point estimation, asymptotics, Bayesian procedure, and deviation theory. Student familiarity with standard statistical techniques is assumed.
Author | : Mark J. Schervish |
Publisher | : Springer Science & Business Media |
Total Pages | : 732 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461242509 |
The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.
Author | : David A. Freedman |
Publisher | : Cambridge University Press |
Total Pages | : 459 |
Release | : 2009-04-27 |
Genre | : Mathematics |
ISBN | : 1139477315 |
This lively and engaging book explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modelling, and the pitfalls. The discussion shows you how to think about the critical issues - including the connection (or lack of it) between the statistical models and the real phenomena. The book is written for advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences.
Author | : Giorgio Alleva |
Publisher | : Springer |
Total Pages | : 306 |
Release | : 2016-05-19 |
Genre | : Mathematics |
ISBN | : 3319272748 |
This book highlights the latest research findings from the 46th International Meeting of the Italian Statistical Society (SIS) in Rome, during which both methodological and applied statistical research was discussed. This selection of fully peer-reviewed papers, originally presented at the meeting, addresses a broad range of topics, including the theory of statistical inference; data mining and multivariate statistical analysis; survey methodologies; analysis of social, demographic and health data; and economic statistics and econometrics.
Author | : D.R. Cox |
Publisher | : CRC Press |
Total Pages | : 525 |
Release | : 1979-09-06 |
Genre | : Mathematics |
ISBN | : 148221492X |
A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistica
Author | : David Roxbee Cox |
Publisher | : Chapman & Hall |
Total Pages | : 216 |
Release | : 1978 |
Genre | : Mathematics |
ISBN | : |
Some general concepts; Pure significance tests; Significance tests: simple null hypotheses; Significance tests: composite null hypotheses; Distribution-free and randomization tests; Interval estimation; Point estimation; Asymptotic theory; Bayesian methods; Decision theory.
Author | : James O. Berger |
Publisher | : Springer Science & Business Media |
Total Pages | : 633 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 147574286X |
In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.
Author | : Helmut Strasser |
Publisher | : Walter de Gruyter |
Total Pages | : 505 |
Release | : 2011-04-20 |
Genre | : Mathematics |
ISBN | : 3110850826 |
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 | : Tailen Hsing |
Publisher | : John Wiley & Sons |
Total Pages | : 363 |
Release | : 2015-05-06 |
Genre | : Mathematics |
ISBN | : 0470016914 |
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.