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Author : M. RAJAGOPALAN
ISBN : 9788120346352
Genre : Mathematics
File Size : 23.93 MB
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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.

Author : James K. Lindsey
ISBN : 0198523599
Genre : Mathematics
File Size : 25.88 MB
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Two central unifying components of statistics are the likelihood function and the exponential family. These are here brought together for the first time as the central themes of a book on statistical inference, appropriate as an advanced undergraduate or graduate text in mathematical statistics.

Author : Paul H. Garthwaite
ISBN : 0198572263
Genre : Mathematics
File Size : 28.68 MB
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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.

Author : George Casella
ISBN : UOM:39015016360508
Genre : Mathematical statistics
File Size : 59.30 MB
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Discusses both theoretical statistics and the practical applications of the theoretical developments. Includes a large numer of exercises covering both theory and applications.

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

Author : Martin A. Tanner
ISBN : 9781468405101
Genre : Medical
File Size : 44.2 MB
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From the reviews: The purpose of the book under review is to give a survey of methods for the Bayesian or likelihood-based analysis of data. The author distinguishes between two types of methods: the observed data methods and the data augmentation ones. The observed data methods are applied directly to the likelihood or posterior density of the observed data. The data augmentation methods make use of the special "missing" data structure of the problem. They rely on an augmentation of the data which simplifies the likelihood or posterior density. #Zentralblatt für Mathematik#

Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Author : A. H. Welsh
ISBN : 0471115916
Genre : Mathematics
File Size : 82.30 MB
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Relevant, concrete, and thorough--the essential data-based text onstatistical 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 expertly synthesizesbroad, critical theory with concrete data and relevant topics. Thetext follows a historical framework, uses real-data sets andstatistical graphics, and treats multiparameter problems, yet isultimately about the concepts themselves. Written with clarity and depth, Aspects of Statistical Inference: * Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches * Illustrates methods with real-data sets on diabetic retinopathy,the pharmacological effects of caffeine, stellar velocity, andindustrial experiments * Considers multiparameter problems * Develops large sample approximations and shows how to use them * Presents the philosophy and application of robustness theory * 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 and presentingthe latest approaches to statistical inference.

Author : Vijay K. Rohatgi
ISBN : 9780486136219
Genre : Mathematics
File Size : 89.39 MB
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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.

Author : Larry Wasserman
ISBN : 9780387217369
Genre : Mathematics
File Size : 79.22 MB
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Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

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.

Author : Michael J. Panik
ISBN : 9781118309803
Genre : Mathematics
File Size : 24.71 MB
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A concise, easily accessible introduction to descriptive and inferential techniques Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures. The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including: How do we determine that a given dataset is actually a random sample? With what level of precision and reliability can a population sample be estimated? How are probabilities determined and are they the same thing as odds? How can we predict the level of one variable from that of another? What is the strength of the relationship between two variables? The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material. Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.

Author : Gudmund R. Iversen
ISBN : 0803923287
Genre : Social Science
File Size : 28.40 MB
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Empirical researchers, for whom Iversen's volume provides an introduction, have generally lacked a grounding in the methodology of Bayesian inference. As a result, applications are few. After outlining the limitations of classical statistical inference, the author proceeds through a simple example to explain Bayes' theorem and how it may overcome these limitations. Typical Bayesian applications are shown, together with the strengths and weaknesses of the Bayesian approach. This monograph thus serves as a companion volume for Henkel's Tests of Significance (QASS vol 4).

Author : Robert B. Ash
ISBN : 9780486481586
Genre : Mathematics
File Size : 40.87 MB
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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.

Author : Rupert G. Jr. Miller
ISBN : 9781461381228
Genre : Mathematics
File Size : 38.54 MB
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Simultaneous Statistical Inference, which was published originally in 1966 by McGraw-Hill Book Company, went out of print in 1973. Since then, it has been available from University Microfilms International in xerox form. With this new edition Springer-Verlag has republished the original edition along with my review article on multiple comparisons from the December 1977 issue of the Journal of the American Statistical Association. This review article covered developments in the field from 1966 through 1976. A few minor typographical errors in the original edition have been corrected in this new edition. A new table of critical points for the studentized maximum modulus is included in this second edition as an addendum. The original edition included the table by K. C. S. Pillai and K. V. Ramachandran, which was meager but the best available at the time. This edition contains the table published in Biometrika in 1971 by G. 1. Hahn and R. W. Hendrickson, which is far more comprehensive and therefore more useful. The typing was ably handled by Wanda Edminster for the review article and Karola Decleve for the changes for the second edition. My wife, Barbara, again cheerfully assisted in the proofreading. Fred Leone kindly granted permission from the American Statistical Association to reproduce my review article. Also, Gerald Hahn, Richard Hendrickson, and, for Biometrika, David Cox graciously granted permission to reproduce the new table of the studentized maximum modulus. The work in preparing the review article was partially supported by NIH Grant ROI GM21215.

Author : Robert Bartoszynski
ISBN : 0470191589
Genre : Mathematics
File Size : 30.90 MB
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Now updated in a valuable new edition—this user-friendly book focuses on understanding the "why" of mathematical statistics Probability and Statistical Inference, Second Edition introduces key probability and statis-tical concepts through non-trivial, real-world examples and promotes the developmentof intuition rather than simple application. With its coverage of the recent advancements in computer-intensive methods, this update successfully provides the comp-rehensive tools needed to develop a broad understanding of the theory of statisticsand its probabilistic foundations. This outstanding new edition continues to encouragereaders to recognize and fully understand the why, not just the how, behind the concepts,theorems, and methods of statistics. Clear explanations are presented and appliedto various examples that help to impart a deeper understanding of theorems and methods—from fundamental statistical concepts to computational details. Additional features of this Second Edition include: A new chapter on random samples Coverage of computer-intensive techniques in statistical inference featuring Monte Carlo and resampling methods, such as bootstrap and permutation tests, bootstrap confidence intervals with supporting R codes, and additional examples available via the book's FTP site Treatment of survival and hazard function, methods of obtaining estimators, and Bayes estimating Real-world examples that illuminate presented concepts Exercises at the end of each section Providing a straightforward, contemporary approach to modern-day statistical applications, Probability and Statistical Inference, Second Edition is an ideal text for advanced undergraduate- and graduate-level courses in probability and statistical inference. It also serves as a valuable reference for practitioners in any discipline who wish to gain further insight into the latest statistical tools.