Principles of Statistical Inference

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Author: D. R. Cox

Publisher: Cambridge University Press

ISBN: 0521685672

Category: Business & Economics

Page: 219

View: 6261

A comprehensive, balanced account of the theory of statistical inference, its main ideas and controversies.

Principles of Statistical Inference

From a Neo-Fisherian Perspective

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Author: Luigi Pace,Alessandra Salvan

Publisher: World Scientific

ISBN: 9789812386946

Category: Mathematics

Page: 535

View: 5349

In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term ?neo-Fisherian? highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.

Aspects of Statistical Inference

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Author: A. H. Welsh

Publisher: John Wiley & Sons

ISBN: 9780471115915

Category: Mathematics

Page: 451

View: 9093

Relevant, concrete, and thorough—the essential data-basedtext on statistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertlysynthesizes broad, critical theory with concrete data and relevanttopics. The text follows a historical framework, uses real-datasets and statistical graphics, and treats multiparameter problems,yet is ultimately about the concepts themselves. Written with clarity and depth, Aspects of StatisticalInference: Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches Illustrates methods with real-data sets on diabeticretinopathy, the pharmacological effects of caffeine, stellarvelocity, and industrial experiments Considers multiparameter problems Develops large sample approximations and shows how to usethem Presents the philosophy and application of robustnesstheory Highlights the central role of randomization in statistics Uses simple proofs to illuminate foundational concepts Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing andpresenting the latest approaches to statistical inference.

Essentials of Statistical Inference

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Author: G. A. Young,R. L. Smith,R. L. (University of North Carolina Smith, Chapel Hill)

Publisher: Cambridge University Press

ISBN: 9780521839716

Category: Mathematics

Page: 225

View: 7683

Concise account of main approaches; first textbook to synthesize modern computation with basic theory.

Principles of Statistics

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Author: M. G. Bulmer

Publisher: Courier Corporation

ISBN: 0486135209

Category: Mathematics

Page: 256

View: 3525

Concise description of classical statistics, from basic dice probabilities to modern regression analysis. Equal stress on theory and applications. Moderate difficulty; only basic calculus required. Includes problems with answers.

Logic of Statistical Inference

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Author: Ian Hacking

Publisher: Cambridge University Press

ISBN: 1107144957

Category: Mathematics

Page: 229

View: 6308

This book showcases Ian Hacking's early ideas on the central issues surrounding statistical reasoning. Presented in a fresh twenty-first-century series livery, and with a specially commissioned new preface, this influential work is now available for a new generation of readers in statistics, philosophy of science and philosophy of maths.

Introduction to the Theory of Statistical Inference

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Author: Hannelore Liero,Silvelyn Zwanzig

Publisher: CRC Press

ISBN: 1466503203

Category: Mathematics

Page: 284

View: 3270

Based on the authors’ lecture notes, Introduction to the Theory of Statistical Inference presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems. Highlights Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form Classroom-tested and designed for students of mathematical statistics Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material Solutions provided for problems formulated at the end of each chapter Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models Theoretical, difficult, or frequently misunderstood problems are marked The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.

Principles of Applied Statistics

An Integrated Approach Using MINITAB and Excel

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Author: Michael C. Fleming,Joseph G. Nellis

Publisher: Cengage Learning EMEA

ISBN: 9781861525864

Category: Business & Economics

Page: 474

View: 6844

This guide examines the principles of statistical data, probability, regression and correlation analysis, forecasting and time-series analysis, emphasizing their practical applications.

Inference Principles for Biostatisticians

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Author: Ian C. Marschner

Publisher: CRC Press

ISBN: 1482222248

Category: Mathematics

Page: 274

View: 8841

Designed for students training to become biostatisticians as well as practicing biostatisticians, Inference Principles for Biostatisticians presents the theoretical and conceptual foundations of biostatistics. It covers the theoretical underpinnings essential to understanding subsequent core methodologies in the field. Drawing on his extensive experience teaching graduate-level biostatistics courses and working in the pharmaceutical industry, the author explains the main principles of statistical inference with many examples and exercises. Extended examples illustrate key concepts in depth using a specific biostatistical context. In addition, the author uses simulation to reinforce the repeated sampling interpretation of numerous statistical concepts. Reducing the computational complexities, he provides simple R functions for conducting simulation studies. This text gives graduate students with diverse backgrounds across the health, medical, social, and mathematical sciences a solid, unified foundation in the principles of statistical inference. This groundwork will lead students to develop a thorough understanding of biostatistical methodology.

Probability and Statistical Inference

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Author: Nitis Mukhopadhyay

Publisher: CRC Press

ISBN: 9780824703790

Category: Mathematics

Page: 665

View: 5343

Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning with an introduction to the basic ideas and techniques in probability theory and progressing to more rigorous topics, Probability and Statistical Inference studies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributions develops notions of convergence in probability and distribution spotlights the central limit theorem (CLT) for the sample variance introduces sampling distributions and the Cornish-Fisher expansions concentrates on the fundamentals of sufficiency, information, completeness, and ancillarity explains Basu's Theorem as well as location, scale, and location-scale families of distributions covers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequality discusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theorems focuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervals includes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficient summarizes Bayesian methods describes the monotone likelihood ratio (MLR) property handles variance stabilizing transformations provides a historical context for statistics and statistical discoveries showcases great statisticians through biographical notes Employing over 1400 equations to reinforce its subject matter, Probability and Statistical Inference is a groundbreaking text for first-year graduate and upper-level undergraduate courses in probability and statistical inference who have completed a calculus prerequisite, as well as a supplemental text for classes in Advanced Statistical Inference or Decision Theory.