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Author: D.R. Cox
Publisher: CRC Press
ISBN: 9780412161605
Category : Mathematics
Languages : en
Pages : 1060
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Book Description
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: D.R. Cox
Publisher: CRC Press
ISBN: 9780412161605
Category : Mathematics
Languages : en
Pages : 1060
Get Book
Book Description
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: Robert W. Keener
Publisher: Springer Science & Business Media
ISBN: 0387938397
Category : Mathematics
Languages : en
Pages : 538
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Book Description
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: Mark J. Schervish
Publisher: Springer Science & Business Media
ISBN: 1461242509
Category : Mathematics
Languages : en
Pages : 732
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Book Description
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: Olga Korotkova
Publisher: World Scientific
ISBN: 981123499X
Category : Science
Languages : en
Pages : 336
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Book Description
This monograph overviews classic and recent developments in theoretical statistical optics in connection with stationary and non-stationary (pulsed) optical source characterization and modeling, discusses various phenomena occurring with random light propagating in free space, on its interaction with optical systems, extended media and particulate collections. The text includes scalar, beam-like and general electromagnetic treatment of light. A brief statistical description of four fundamental experiments relating to random light: spatial and temporal field interference, intensity interferometry and phase conjugation, is also included in order to relate the analytical descriptions with practical observations.Rigorous mathematical methods for statistical manipulation of light sources useful for remote shaping of its various average properties, enhanced image resolution, optimized transmission in random media and for other applications are introduced. For illustration of efficient ways for manipulation of light polarization the generalized Stokes-Mueller calculus is applied for description of interaction of beam-like fields with classic and currently popular devices of polarization optics, including a spatial light modulator.Random light plays a special role in the image formation process. Three imaging modalities including the classic intensity-based system with structured source correlations, the polarization-based imaging system and the ghost interference approach are discussed in detail.Theoretical aspects of potential scattering of light from weakly scattering media are considered under a very broad range of assumptions: scalar/electromagnetic incident light, deterministic/random light/media, single/particulate media. Then, problems and methods in light characterization on interaction with extended, turbulent-like natural media, such as the Earth's atmosphere, oceans and soft bio-tissues that are currently widely used for communication, remote sensing and imaging purposes in these media, are provided.
Author: David A. Freedman
Publisher: Cambridge University Press
ISBN: 9781139477314
Category : Mathematics
Languages : en
Pages :
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Book Description
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: Paul Meehl
Publisher: Echo Point Books & Media
ISBN: 9781626542303
Category : Medical
Languages : en
Pages : 164
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Book Description
"Clinical versus Statistical Prediction" is Paul Meehl's famous examination of benefits and disutilities related to the different ways of combining information to make predictions. It is a clarifying analysis as relevant today as when it first appeared. A major methodological problem for clinical psychology concerns the relation between clinical and actuarial methods of arriving at diagnoses and predicting behavior. Without prejudging the question as to whether these methods are fundamentally different, we can at least set forth the obvious distinctions between them in practical applications. The problem is to predict how a person is going to behave: What is the most accurate way to go about this task? "Clinical versus Statistical Prediction" offers a penetrating and thorough look at the pros and cons of human judgment versus actuarial integration of information as applied to the prediction problem. Widely considered the leading text on the subject, Paul Meehl's landmark analysis is reprinted here in its entirety, including his updated preface written forty-two years after the first publication of the book. This classic work is a must-have for students and practitioners interested in better understanding human behavior, for anyone wanting to make the most accurate decisions from all sorts of data, and for those interested in the ethics and intricacies of prediction. As Meehl puts it, " "When one is dealing with human lives and life opportunities, it is immoral to adopt a mode of decision-making which has been demonstrated repeatedly to be either inferior in success rate or, when equal, costlier to the client or the taxpayer.""
Author: George Casella
Publisher: CRC Press
ISBN: 1040024025
Category : Mathematics
Languages : en
Pages : 1746
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Book Description
This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.
Author: Giorgio Alleva
Publisher: Springer
ISBN: 3319272748
Category : Mathematics
Languages : en
Pages : 315
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Book Description
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: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 0470016914
Category : Mathematics
Languages : en
Pages : 362
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Book Description
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.
Author: Martin J. Wainwright
Publisher: Cambridge University Press
ISBN: 1108498027
Category : Business & Economics
Languages : en
Pages : 571
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Book Description
A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
