Statistical Theory And Inference
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Statistical Theory And Inference
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Author : David Olive
language : en
Publisher:
Release Date : 2014-05-31
Statistical Theory And Inference written by David Olive and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-31 with categories.
Statistical Theory And Inference
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Author : David J. Olive
language : en
Publisher: Springer
Release Date : 2014-05-07
Statistical Theory And Inference written by David J. Olive and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-07 with Mathematics categories.
This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.
Some Basic Theory For Statistical Inference
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Author : E.J.G. Pitman
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Some Basic Theory For Statistical Inference written by E.J.G. Pitman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
In this book the author presents with elegance and precision some of the basic mathematical theory required for statistical inference at a level which will make it readable by most students of statistics.
Foundations And Philosophy Of Epistemic Applications Of Probability Theory
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Author : W.L. Harper
language : en
Publisher: Springer Science & Business Media
Release Date : 1976
Foundations And Philosophy Of Epistemic Applications Of Probability Theory written by W.L. Harper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Gardening categories.
Proceedings of an International Research Colloquium held at the University of Western Ontario, 10-13 May 1973.
Statistical Theory And Modelling
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Author : D.V. Hinkley
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1991
Statistical Theory And Modelling written by D.V. Hinkley and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Statistical Theory and Modelling is a celebration of the work of Sir David Cox, FRS, and reflects his many interests in statistical theory and methods. It is a series of review articles, intended as an introduction to a variety of topics suitable for the graduate student and practicing statistician. Many of the topics are the subject of book-length treatments by Sir David and authors of this volume. Each chapter leads to a larger literature. Topics range the breadth of statistics and include modern degvelopments in statistical theory and methods. Special topics covered are generalized linear models, residuals and diagnostics, survival analysis, sequential analysis, time series, stochastic modelling of spatial data, design of experiments, likelihood inference and statistical approximation.
Foundations Of Probability Theory Statistical Inference And Statistical Theories Of Science
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Author : W.L. Harper
language : en
Publisher: Springer
Release Date : 1975-12-31
Foundations Of Probability Theory Statistical Inference And Statistical Theories Of Science written by W.L. Harper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-12-31 with Science categories.
In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory. The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Bayesian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference. Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.
Theory Of Statistical Inference
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Author : Anthony Almudevar
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Theory Of Statistical Inference written by Anthony Almudevar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.
Introduction To The Theory Of Statistical Inference
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Author : Hannelore Liero
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Introduction To The Theory Of Statistical Inference written by Hannelore Liero and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.
Introduction To Probability Theory And Statistical Inference
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Author : Harold J. Larson
language : en
Publisher:
Release Date : 1969
Introduction To Probability Theory And Statistical Inference written by Harold J. Larson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Logic Of Statistical Inference
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Author : Ian Hacking
language : en
Publisher: Cambridge University Press
Release Date : 1965-01-01
Logic Of Statistical Inference written by Ian Hacking and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965-01-01 with Philosophy categories.
This book is a philosophical study of the basic principles of statistical reasoning. Professor Hacking has sought to discover the simple principles which underlie modern work in mathematical statistics and to test them, both at a philosophical level and in terms of their practical consequences fort statisticians. The ideas of modern logic are used to analyse these principles, and results are presented without the use of unfamiliar symbolism. It begins with a philosophical analysis of a few central concepts and then, using an elementary system of logic, develops most of the standard statistical theory. the analysis provides answers to many disputed questions about how to test statistical hypotheses and about how to estimate quantities in the light of statistical data. One product of the analysis is a sound and consistent rationale for R. A. Fisher's controversial concept of 'fiducial probability'.