Aspects of Statistical Inference

Author: A. H. Welsh

Publisher: John Wiley & Sons

ISBN: 9780471115915

Category: Mathematics

Page: 451

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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.

Sense and Nonsense of Statistical Inference

Controversy: Misuse, and Subtlety

Author: Charmont Wang

Publisher: CRC Press

ISBN: 9780824787981

Category: Mathematics

Page: 256

View: 1365

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This volume focuses on the abuse of statistical inference in scientific and statistical literature, as well as in a variety of other sources, presenting examples of misused statistics to show that many scientists and statisticians are unaware of, or unwilling to challenge the chaotic state of statistical practices.;The book: provides examples of ubiquitous statistical tests taken from the biomedical and behavioural sciences, economics and the statistical literature; discusses conflicting views of randomization, emphasizing certain aspects of induction and epistemology; reveals fallacious practices in statistical causal inference, stressing the misuse of regression models and time-series analysis as instant formulas to draw causal relationships; treats constructive uses of statistics, such as a modern version of Fisher's puzzle, Bayesian analysis, Shewhart control chart, descriptive statistics, chi-square test, nonlinear modeling, spectral estimation and Markov processes in quality control.

Statistical Inference

Author: S.D. Silvey

Publisher: Routledge

ISBN: 135141450X

Category: Mathematics

Page: 192

View: 7345

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Statistics is a subject with a vast field of application, involving problems which vary widely in their character and complexity.However, in tackling these, we use a relatively small core of central ideas and methods. This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the extraneous difficulties of complicatedmathematical manipulation.In order to compress the central body of ideas into a smallvolume, it is necessary to assume a fair degree of mathematicalsophistication on the part of the reader, and the book is intendedfor students of mathematics who are already accustomed tothinking in rather general terms about spaces and functions

STATISTICAL INFERENCE

Author: M. RAJAGOPALAN,P. DHANAVANTHAN

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120346351

Category: Mathematics

Page: 408

View: 1286

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Intended as a text for the postgraduate students of statistics, this well-written book gives a complete coverage of Estimation theory and Hypothesis testing, in an easy-to-understand style. It is the outcome of the authors’ teaching experience over the years. The text discusses absolutely continuous distributions and random sample which are the basic concepts on which Statistical Inference is built up, with examples that give a clear idea as to what a random sample is and how to draw one such sample from a distribution in real-life situations. It also discusses maximum-likelihood method of estimation, Neyman’s shortest confidence interval, classical and Bayesian approach. The difference between statistical inference and statistical decision theory is explained with plenty of illustrations that help students obtain the necessary results from the theory of probability and distributions, used in inference.

Statistical Inference

Author: Paul H. Garthwaite,I. T. Jolliffe,Byron Jones

Publisher: Oxford University Press on Demand

ISBN: 9780198572268

Category: Mathematics

Page: 328

View: 6639

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Statistical inference is the foundation on which much of statistical practice is built. This book covers the topic at a level suitable for students and professionals who need to understand these foundations.

Statistical Inference in Science

Author: D.A. Sprott

Publisher: Springer Science & Business Media

ISBN: 9780387950198

Category: Mathematics

Page: 248

View: 3254

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A treatment of the problems of inference associated with experiments in science, with the emphasis on techniques for dividing the sample information into various parts, such that the diverse problems of inference that arise from repeatable experiments may be addressed. A particularly valuable feature is the large number of practical examples, many of which use data taken from experiments published in various scientific journals. This book evolved from the authors own courses on statistical inference, and assumes an introductory course in probability, including the calculation and manipulation of probability functions and density functions, transformation of variables and the use of Jacobians. While this is a suitable text book for advanced undergraduate, Masters, and Ph.D. statistics students, it may also be used as a reference book.

Parametric Statistical Inference

Author: James K. Lindsey

Publisher: Oxford University Press

ISBN: 9780198523598

Category: Mathematics

Page: 490

View: 1172

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Inference involves drawing conclusions about some general phenomenon from limited empirical observations in the face of random variability. Two central unifying components of statistics are the likelihood function and the exponential family. These are here brought together for the firsttime as the central themes of a book on statistical inference. This book is appropriate as an advanced undergraduate or graduate text in mathematical statistics.

Introduction to Statistical Inference

Author: E. S. Keeping

Publisher: Courier Corporation

ISBN: 9780486685021

Category: Mathematics

Page: 451

View: 8044

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This excellent text emphasizes the inferential and decision-making aspects of statistics. The first chapter is mainly concerned with the elements of the calculus of probability. Additional chapters cover the general properties of distributions, testing hypotheses, and more.

Probability and Statistical Inference

Author: Nitis Mukhopadhyay

Publisher: CRC Press

ISBN: 9780824703790

Category: Mathematics

Page: 665

View: 3787

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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.

Tools for Statistical Inference

Methods for the Exploration of Posterior Distributions and Likelihood Functions

Author: Martin A. Tanner

Publisher: Springer

ISBN: 0387946888

Category: Mathematics

Page: 220

View: 350

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A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

Statistical Inference

A Short Course

Author: Michael J. Panik

Publisher: John Wiley & Sons

ISBN: 1118309804

Category: Mathematics

Page: 400

View: 2148

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A concise, easily accessible introduction to descriptiveand inferential techniques Statistical Inference: A Short Course offers a concisepresentation of the essentials of basic statistics for readersseeking to acquire a working knowledge of statistical concepts,measures, and procedures. The author conducts tests on the assumption of randomness andnormality, provides nonparametric methods when parametricapproaches might not work. The book also explores how to determinea confidence interval for a population median while also providingcoverage of ratio estimation, randomness, and causality. To ensurea thorough understanding of all key concepts, StatisticalInference provides numerous examples and solutions along withcomplete and precise answers to many fundamental questions,including: How do we determine that a given dataset is actually a randomsample? With what level of precision and reliability can a populationsample be estimated? How are probabilities determined and are they the same thing asodds? How can we predict the level of one variable from that ofanother? What is the strength of the relationship between twovariables? The book is organized to present fundamental statisticalconcepts first, with later chapters exploring more advanced topicsand additional statistical tests such as Distributional Hypotheses,Multinomial Chi-Square Statistics, and the Chi-Square Distribution.Each chapter includes appendices and exercises, allowing readers totest their comprehension of the presented material. Statistical Inference: A Short Course is an excellentbook for courses on probability, mathematical statistics, andstatistical inference at the upper-undergraduate and graduatelevels. The book also serves as a valuable reference forresearchers and practitioners who would like to develop furtherinsights into essential statistical tools.

STATISTICAL INFERENCE : THEORY OF ESTIMATION

Author: MANOJ KUMAR SRIVASTAVA,ABDUL HAMID KHAN,NAMITA SRIVASTAVA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 812034930X

Category: Mathematics

Page: 808

View: 3588

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This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimator based on a sufficient statistic and Lehmann-Scheffe theorem to give an UMVUE. It discusses Cramer-Rao and Bhattacharyya variance lower bounds for regular models, by introducing Fishers information and Chapman, Robbins and Kiefer variance lower bounds for Pitman models. Besides, the book introduces different methods of estimation including famous method of maximum likelihood and discusses large sample properties such as consistency, consistent asymptotic normality (CAN) and best asymptotic normality (BAN) of different estimators. Separate chapters are devoted for finding Pitman estimator, among equivariant estimators, for location and scale models, by exploiting symmetry structure, present in the model, and Bayes, Empirical Bayes, Hierarchical Bayes estimators in different statistical models. Systematic exposition of the theory and results in different statistical situations and models, is one of the several attractions of the presentation. Each chapter is concluded with several solved examples, in a number of statistical models, augmented with exposition of theorems and results. KEY FEATURES • Provides clarifications for a number of steps in the proof of theorems and related results., • Includes numerous solved examples to improve analytical insight on the subject by illustrating the application of theorems and results. • Incorporates Chapter-end exercises to review student’s comprehension of the subject. • Discusses detailed theory on data summarization, unbiased estimation with large sample properties, Bayes and Minimax estimation, separately, in different chapters.

Statistical Inference

Author: Vijay K. Rohatgi

Publisher: Courier Corporation

ISBN: 0486136213

Category: Mathematics

Page: 956

View: 5648

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This treatment of probability and statistics examines discrete and continuous models, functions of random variables and random vectors, large-sample theory, more. Hundreds of problems (some with solutions). 1984 edition. Includes 144 figures and 35 tables.

Philosophical Problems of Statistical Inference

Learning from R.A. Fisher

Author: T. Seidenfeld

Publisher: Springer Science & Business Media

ISBN: 9789027709653

Category: Social Science

Page: 247

View: 1795

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Probability and inverse inference; Neyman-Pearson theory; Fisherian significance testing; The fiducial argument: one parameter; The fiducial argument: several parameters; Ian hacking's theory; Henry Kyburg's theory; Relevance and experimental design.

Statistical Inference

A Concise Course

Author: Robert B. Ash

Publisher: Courier Corporation

ISBN: 0486481581

Category: Mathematics

Page: 124

View: 8759

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This book offers a brief course in statistical inference that requires only a basic familiarity with probability and matrix and linear algebra. Ninety problems with solutions make it an ideal choice for self-study as well as a helpful review of a wide-ranging topic with important uses to professionals in business, government, public administration, and other fields. 2011 edition.

Principles of Statistical Inference

Author: D. R. Cox

Publisher: Cambridge University Press

ISBN: 9781139459136

Category: Mathematics

Page: N.A

View: 6954

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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.

Linear Statistical Inference and its Applications

Author: C. Radhakrishna Rao

Publisher: John Wiley & Sons

ISBN: 0470317140

Category: Mathematics

Page: 656

View: 8116

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"C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistical theory." -W. G. Cochran "[C. R. Rao is] one of the pioneers who laid the foundations of statistics which grew from ad hoc origins into a firmly grounded mathematical science." -B. Efrom Translated into six major languages of the world, C. R. Rao's Linear Statistical Inference and Its Applications is one of the foremost works in statistical inference in the literature. Incorporating the important developments in the subject that have taken place in the last three decades, this paperback reprint of his classic work on statistical inference remains highly applicable to statistical analysis. Presenting the theory and techniques of statistical inference in a logically integrated and practical form, it covers: * The algebra of vectors and matrices * Probability theory, tools, and techniques * Continuous probability models * The theory of least squares and the analysis of variance * Criteria and methods of estimation * Large sample theory and methods * The theory of statistical inference * Multivariate normal distribution Written for the student and professional with a basic knowledge of statistics, this practical paperback edition gives this industry standard new life as a key resource for practicing statisticians and statisticians-in-training.

Nonparametric Statistical Inference

Author: Jean Dickinson Gibbons,Subhabrata Chakraborti

Publisher: CRC Press

ISBN: 0824755227

Category: Mathematics

Page: 680

View: 9149

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Thoroughly revised and reorganized, the fourth edition presents in-depth coverage of the theory and methods of the most widely used nonparametric procedures in statistical analysis and offers example applications appropriate for all areas of the social, behavioral, and life sciences. The book presents new material on the quantiles, the calculation of exact and simulated power, multiple comparisons, additional goodness-of-fit tests, methods of analysis of count data, and modern computer applications using MINITAB, SAS, and STATXACT. It includes tabular guides for simplified applications of tests and finding P values and confidence interval estimates.