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8. An Introduction to the Bootstrap

8. An Introduction to the Bootstrap 1995] REVIEWS 347 8. An Introduction to the Bootstrap. By B. Efron and R. J. Tibshirani. ISBN 041204231 2. Chapman and Hall, London, 1993. 436 pp. £29.95. This book aims to be an introduction to the theory and application of the bootstrap and other resampling methods, which the authors themselves have done much to pioneer. The book could be used for teaching in several ways. The first two-thirds, for example, could form the basis of an advanced undergraduate course introducing and applying resampling methods with the minimum of theoretical baggage. The final sections of the book contain more advanced material aimed at a more statistically sophisticated audience, and so the complete book could form the core of a graduate level course. I found that I thoroughly enjoyed reading this book. I came to it with just a smattering of knowledge of the folklore of the bootstrap, but its easily accessible style and its careful use throughout of examples and illustrations rapidly transmit the essentials of the subject. The book assumes little background in the use of statistical methods although I doubt whether an audience with absolutely no experience would find it completely straightforward. It progresses, by use often of examples, to consider how the bootstrap calculates standard errors, as well as issues of bias and hypothesis testing. It considers applications to regression models and compares the bootstrap with the jackknife and other resampling methods. The end of the book contains the more advanced material, e.g, a geometrical interpretation of resampling, which was particularly well done, efficient computation, more sophisticated resampling strategies and applications to likelihood methods. There is also an appendix on software and how to programme for the implementation of these ideas. My overall reaction was very positive. I particularly liked the use of very clear and well-thought-out graphical plots to illustrate the examples. I came away from the book looking for some students to try it out on. I shall be interested in their reaction. Paul Marriott University of Surrey Guildford 9. Competitive Equilibrium: Theory and Applications. By B. Ellickson. ISBN 0521266602 (hardbound), 0 521319889 (paperbound). Cambridge University Press, Cambridge, 1994. xx+394pp. £35.00 (hardbound), £14.95 (paperbound). Two difficulties face the proponents of equilibrium theory. One is convincing other economists that the various types of equilibrium are relevant to real life, and the other is the level of mathematics needed-locally convex topological vector spaces do not come naturally to the minds of most people. This book faces the second of these difficulties squarely and successfully. An example of Ellickson's philosophy is in the introduction to Chapter 6: 'Why bother with existence? . . . the conclusion reported in an existence proof is of secondary importance. What really matters is the understanding gained in proving the result'. Chapter 1 introduces Walrasian equilibrium, and from there the book branches out, finishing with Debreu-Scarf equivalence and the Anderson theorem. Each step introduces its own assumptions and consequences for the model economy, and the author's view is that the details of any mathematical result (usually an existence or continuity proof) must reflect some property of the model under consideration. This approach means that a surprising range of mathematics is needed. We start with set theory and linear algebra in Chapter 1, convexity in Chapter 2 and Lebesgue integration and measure spaces in Chapter 3. Chapter 4 has nearly 40 pages devoted entirely to topology. Chapter 5 uses continuity in topological spaces, Chapter 6 simplices and Chapter 8 lattices. All must be explained from scratch. This is done rigorously http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Royal Statistical Society Series A (Statistics in Society) Oxford University Press

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Copyright
© 1995 Royal Statistical Society
ISSN
0964-1998
eISSN
1467-985X
DOI
10.2307/2983304
Publisher site
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Abstract

1995] REVIEWS 347 8. An Introduction to the Bootstrap. By B. Efron and R. J. Tibshirani. ISBN 041204231 2. Chapman and Hall, London, 1993. 436 pp. £29.95. This book aims to be an introduction to the theory and application of the bootstrap and other resampling methods, which the authors themselves have done much to pioneer. The book could be used for teaching in several ways. The first two-thirds, for example, could form the basis of an advanced undergraduate course introducing and applying resampling methods with the minimum of theoretical baggage. The final sections of the book contain more advanced material aimed at a more statistically sophisticated audience, and so the complete book could form the core of a graduate level course. I found that I thoroughly enjoyed reading this book. I came to it with just a smattering of knowledge of the folklore of the bootstrap, but its easily accessible style and its careful use throughout of examples and illustrations rapidly transmit the essentials of the subject. The book assumes little background in the use of statistical methods although I doubt whether an audience with absolutely no experience would find it completely straightforward. It progresses, by use often of examples, to consider how the bootstrap calculates standard errors, as well as issues of bias and hypothesis testing. It considers applications to regression models and compares the bootstrap with the jackknife and other resampling methods. The end of the book contains the more advanced material, e.g, a geometrical interpretation of resampling, which was particularly well done, efficient computation, more sophisticated resampling strategies and applications to likelihood methods. There is also an appendix on software and how to programme for the implementation of these ideas. My overall reaction was very positive. I particularly liked the use of very clear and well-thought-out graphical plots to illustrate the examples. I came away from the book looking for some students to try it out on. I shall be interested in their reaction. Paul Marriott University of Surrey Guildford 9. Competitive Equilibrium: Theory and Applications. By B. Ellickson. ISBN 0521266602 (hardbound), 0 521319889 (paperbound). Cambridge University Press, Cambridge, 1994. xx+394pp. £35.00 (hardbound), £14.95 (paperbound). Two difficulties face the proponents of equilibrium theory. One is convincing other economists that the various types of equilibrium are relevant to real life, and the other is the level of mathematics needed-locally convex topological vector spaces do not come naturally to the minds of most people. This book faces the second of these difficulties squarely and successfully. An example of Ellickson's philosophy is in the introduction to Chapter 6: 'Why bother with existence? . . . the conclusion reported in an existence proof is of secondary importance. What really matters is the understanding gained in proving the result'. Chapter 1 introduces Walrasian equilibrium, and from there the book branches out, finishing with Debreu-Scarf equivalence and the Anderson theorem. Each step introduces its own assumptions and consequences for the model economy, and the author's view is that the details of any mathematical result (usually an existence or continuity proof) must reflect some property of the model under consideration. This approach means that a surprising range of mathematics is needed. We start with set theory and linear algebra in Chapter 1, convexity in Chapter 2 and Lebesgue integration and measure spaces in Chapter 3. Chapter 4 has nearly 40 pages devoted entirely to topology. Chapter 5 uses continuity in topological spaces, Chapter 6 simplices and Chapter 8 lattices. All must be explained from scratch. This is done rigorously

Journal

Journal of the Royal Statistical Society Series A (Statistics in Society)Oxford University Press

Published: Dec 5, 2018

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