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Essentials of Statistical Inference
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Young & Smith
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Cambridge
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1 edition
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236 pages
ISBN
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0521839718
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2,244 Point
This textbook presents the concepts and results underlying the Bayesian, frequentist, and Fisherian approaches to statistical inference, with particular emphasis on the contrasts between them. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it covers basic mathematical theory as well as more advanced material, including such contemporary topics as Bayesian computation, higher-order likelihood theory, predictive inference, bootstrap methods, and conditional inference.
1. Decision theory;
2. Bayesian methods;
3. Hypothesis testing;
4. Special models;
5. Sufficiency and completeness;
6. Two-sided tests and conditional inference;
7. Likelihood theory;
8. Higher-order theory;
9. Predictive inference;
10. Bootstrap methods;
References;
Index.
"There are many excellent books for a first graduate level course in mathematical statistics. It is quite common to see texts such as Lehmann's book on hypothesis testing and his second one on estimation based on the frequentist approach. There are also at this time, many books written from the Bayesian approach with DeGroot's being one of the earliest. At this time it is rare to see a text written from the Fisherian approach partly because the concept of fiducial inference has largely been discredited. Of course Fisher's texts were written from his perspective although not always so clearly illucidated.
This book is very unique in that the authors present the foundations of all three schools of inference and produce the essential theoretical results in each approach. The book is concise but provides the key theorems and results of the methods developed in the 20th century. It includes many of the modern advances of the latter portion of the twentieth century from 1980 - 2000. This includes resampling methods especially the bootstrap which has its own chapter (Chapter 11).
The book also contains a great bibliography that is partially annotated. Readers should pay attention to the annotations as they are very enlightening. Another computer-intensive method, Markov Chain Monte Carlo, is covered under the Bayesian paradigm where it has very important applications. This book could easily be used for a modern first graduate level course in mathematical statistics."
"Statistical inference is arguably the most fundamental statistical technique used in the world. When I teach a basic statistics course, we spend half the term doing inference problems. The formal theory behind inference is an integral part of mathematics and this book covers the key ideas of the Bayesian, frequentist and Fisherian approaches. Advertised as written at the level of advanced undergraduates and graduate students, I concur with that assessment. The material is accessible to the senior math major, although I disagree with the sentence on the cover, "Some prior knowledge of probability is assumed, while some previous knowledge of the objectives and main approaches to statistical inference would be helpful but is not essential." To understand this book, it is necessary that the reader have a good understanding of what inference is and better yet, should have already done several inference problems. Experience in multivariable calculus and the functions of commonly used statistical distributions are also essential.
Some of the more advanced topics include:
*) Bayesian computation.
*) Higher-order liklihood theory.
*) Predictive inference.
*) Bootstrap methods.
*) Conditional inference.
This is a solid book, ideal for advanced classes in the mathematical justification for statistical inference
Published in Journal of Recreational Mathematics, reprinted with permission."
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