Download or read book Theory of Statistical Inference written by Anthony Almudevar and published by CRC Press. This book was released on 2021-12-30 with total page 1059 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Statistical Inference written by George Casella and published by CRC Press. This book was released on 2024-05-23 with total page 1746 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to the Theory of Statistical Inference written by Hannelore Liero and published by CRC Press. This book was released on 2016-04-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Models for Probability and Statistical Inference written by James H. Stapleton and published by John Wiley & Sons. This book was released on 2007-12-14 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.

Download or read book Probability Theory and Statistical Inference written by Aris Spanos and published by Cambridge University Press. This book was released on 2019-09-19 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: This empirical research methods course enables informed implementation of statistical procedures, giving rise to trustworthy evidence.

Download or read book Principles of Statistical Inference written by D. R. Cox and published by Cambridge University Press. This book was released on 2006-08-10 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.

Download or read book Unifying Political Methodology written by Gary King and published by University of Michigan Press. This book was released on 1998-06-24 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVArgues that likelihood theory is a unifying approach to statistical modeling in political science /div

Download or read book Some Basic Theory for Statistical Inference written by E.J.G. Pitman and published by CRC Press. This book was released on 2018-01-18 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Statistical Inference as Severe Testing written by Deborah G. Mayo and published by Cambridge University Press. This book was released on 2018-09-20 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.

Download or read book Statistical Theory and Inference written by David J. Olive and published by Springer. This book was released on 2014-05-07 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Theory of Statistical Inference and Information written by Igor Vajda and published by Springer. This book was released on 1989-02-28 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Essential Statistical Inference written by Dennis D. Boos and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods. ​

Download or read book The Myth of Statistical Inference written by Michael C. Acree and published by Springer Nature. This book was released on 2021-07-05 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes and explores the idea that the forced union of the aleatory and epistemic aspects of probability is a sterile hybrid, inspired and nourished for 300 years by a false hope of formalizing inductive reasoning, making uncertainty the object of precise calculation. Because this is not really a possible goal, statistical inference is not, cannot be, doing for us today what we imagine it is doing for us. It is for these reasons that statistical inference can be characterized as a myth. The book is aimed primarily at social scientists, for whom statistics and statistical inference are a common concern and frustration. Because the historical development given here is not merely anecdotal, but makes clear the guiding ideas and ambitions that motivated the formulation of particular methods, this book offers an understanding of statistical inference which has not hitherto been available. It will also serve as a supplement to the standard statistics texts. Finally, general readers will find here an interesting study with implications far beyond statistics. The development of statistical inference, to its present position of prominence in the social sciences, epitomizes a number of trends in Western intellectual history of the last three centuries, and the 11th chapter, considering the function of statistical inference in light of our needs for structure, rules, authority, and consensus in general, develops some provocative parallels, especially between epistemology and politics.

Download or read book The Theory and Applications of Statistical Interference Functions written by D.L. McLeish and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph arose out of a desire to develop an approach to statistical infer ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete ness into this setting. The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. This is in keeping with our desire to construct a theory that is rich in statistical tools for infer ence without the difficulties found in modern developments, such as likelihood analysis of stochastic processes or higher order methods, to name but two. The fundamental notions of orthogonality and projection are accessible to a good undergraduate or beginning graduate student. We hope that the monograph will serve the purpose of enriching the methods available to statisticians of various interests.

Download or read book Asymptotic Theory of Statistical Inference for Time Series written by Masanobu Taniguchi and published by Springer. This book was released on 2012-10-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Download or read book Asymptotic Theory Of Quantum Statistical Inference Selected Papers written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.

Download or read book Asymptotic Theory of Statistical Inference written by B. L. S. Prakasa Rao and published by . This book was released on 1987-01-16 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.