Elements of Computational Statistics

1. Front Matter

   Pages i-xviii

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2. Methods of Computational Statistics

   1. Front Matter

      Pages 1-4

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   2. Preliminaries

      Pages 5-36

   3. Monte Carlo Methods for Inference

      Pages 37-65

   4. Randomization and Data Partitioning

      Pages 67-82

   5. Bootstrap Methods

      Pages 83-96

   6. Tools for Identification of Structure in Data

      Pages 97-124

   7. Estimation of Functions

      Pages 125-148

   8. Graphical Methods in Computational Statistics

      Pages 149-186

3. Data Density and Structure

   1. Front Matter

      Pages 187-191

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   2. Estimation of Probability Density Functions Using Parametric Models

      Pages 193-199

   3. Nonparametric Estimation of Probability Density Functions

      Pages 201-224

   4. Structure in Data

      Pages 225-290

   5. Statistical Models of Dependencies

      Pages 291-327

4. Back Matter

   Pages 329-420

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In recent years developments in statistics have to a great extent gone hand in hand with developments in computing. Indeed, many of the recent advances in statistics have been dependent on advances in computer science and techn- ogy. Many of the currently interesting statistical methods are computationally intensive, eitherbecausetheyrequireverylargenumbersofnumericalcompu- tions or because they depend on visualization of many projections of the data. The class of statistical methods characterized by computational intensity and the supporting theory for such methods constitute a discipline called “com- tational statistics”. (Here, I am following Wegman, 1988, and distinguishing “computationalstatistics”from“statisticalcomputing”, whichwetaketomean “computational methods, including numerical analysis, for statisticians”.) The computationally-intensive methods of modern statistics rely heavily on the developments in statistical computing and numerical analysis generally. Computational statistics shares two hallmarks with other “computational” sciences, such as computational physics, computational biology, and so on. One is a characteristic of the methodology: it is computationally intensive. The other is the nature of the tools of discovery. Tools of the scienti?c method have generally been logical deduction (theory) and observation (experimentation). The computer, used to explore large numbers of scenarios, constitutes a new type of tool. Use of the computer to simulate alternatives and to present the research worker with information about these alternatives is a characteristic of thecomputationalsciences. Insomewaysthisusageisakintoexperimentation. The observations, however, are generated from an assumed model, and those simulated data are used toevaluate and study the model.

• Approximation
• Partition
• Resampling
• Ringe
• Statistica
• algebra
• linear algebra
• numerical analysis
• optimization
• probability
• statistics

From the reviews:

TECHNOMETRICS

"For the probable purchasers of this text, I feel that Gentle has succeeded in presenting a broad overview of the major areas of modern computational statistics…In conclusion, I found this book to be a comprehensive summary of computational methods used in modern statistical analyses. It certainly has a place on my bookshelf. The bibliography alone makes it a valuable research tool for those working in this area."

SHORT BOOK REVIEWS

"This book describes many of the exciting, even revolutionary, developments in computational statistics which have been made over the last two or three decades...The book has a rather mainstream statistical feel to it: it gives excellent discussions of topics such as bootstrap methods, density function estimation, and multivariate tools such as principle components, clustering and projection pursuit…It would provide an excellent grounding for someone beginning to work in this area…"

"The book by James Gentle illustrates statistical ideas and computational tools to explore, extract, and test for significance the information in collected data. … The chapters have exercises and solutions. The book is suitable to be a text book in a graduate level course on computational statistics. … I enjoyed reading … and recommend … very highly to the statistical community." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 75 (2), 2005)

"This book provides a wealth of knowledge on the topic of computational statistics … . Gentle’s prose is very readable, with many sections written in an almost conversational style. … I highly recommend this book as a resource … . I wish to commend Gentle for his efforts on this well-written book. The vast coverage of methodology makes this book a valuable resource for any statistician involved with computational statistics … as well as for applied researchers in other fields who useadvanced statistical methods." (Herbert K. H. Lee, Journal of the American Statistical Association, Vol. 98 (463), September, 2003)

"Computational statistics is a collection of methods and techniques in statistics which are computationally intensive and use the computer as a tool for experimentation. … The material covered is extensive. … relevant references are given. The book also contains lots of exercises of varying level … . The writing style in this book is accessible … . Practical aspects are stressed. All in all, the book is valuable for people who want to know something about the strength and applicability of statistical methods ... ." (Dr. G. Jongbloed, Kwantitatieve Methoden, Issue 72B28, 2004)

"The book is devoted to computationally intensive methods of statistical analysis such as resampling, randomization tests or data mining. … the book covers a lot of questions … . So, this … may be a good reference guide on the current state of statistics. The bibliography contains more than 500 items and there are many WWW references in the text." (R. E. Maiboroda, Zentralblatt MATH, Vol. 1031, 2004)

"Gentle defines computational statistics … as ‘the class of statistical methods characterized by computational intensity and the supporting methods for such methods’. … There is good coverage here of an extensive range of statistical methods … . Each chapter is accompanied by a good selection of challenging exercises … . clear descriptions of the fundamentals together with several references to advanced topics for the interested reader. … I will be happy to use it to dip into as a general reference book." (Richard Bolton, Journal of Applied Statistics, Vol. 31 (9), 2004)

"This book grew out of courses on computational statistics that were offered by the author at George Mason University. … The exercises are an important way of adding to the information that is gained from the text. … The presentationis very accessible. Apart from its obvious use as a course text, this is a useful reference for any statistician who uses or wishes to use computationally intensive methods. This is the third of a series … . I have enjoyed reading all of them." (David Kemp, Journal of the Royal Statistical Society, Vol. 157 (3), 2004)

"This book is an audacious undertaking by the author – an effort to present all of the major statistical methods that require a large degree of computational intensity. … I feel that Gentle has succeeded in presenting a broad overview of the major areas of modern computational statistics. … I found this book to be a comprehensive summary of computational methods used in modern statistical analyses. It certainly has a place on my bookshelf. The bibliography alone makes it a valuable research tool … ." (William J. Owen, Technometrics, Vol. 45 (3), 2003)

"This book describes many of the exciting, even revolutionary, developments in computational statistics which have been made over the last two or three decades. … it gives excellent discussions of topics such as bootstrap methods, density function estimation, and multivariate tools such as principal components, clustering and projection pursuit. … It would provide an excellent grounding for someone beginning to work in this area … ." (D. J. Hand, Short Book Reviews, Vol. 23 (1), 2003)

• Department of Computational Sciences and Informatics, George Mason University, Fairfax, USA

  James E. Gentle

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