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An Introduction to the Bootstrap

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Bradley Efron and Robert J. Tibshirani
Publisher: Chapman & Hall/CRC
Copyright: 1993
ISBN-13: 978-0-412-04231-7
Pages: 436; hardcover
Price: $97.50
Bradley Efron and Robert J. Tibshirani
Publisher: Chapman & Hall/CRC
Copyright: 1993
Pages: 436; eBook
Price: $0.00

Comment from the Stata technical group

In 1979, Bradley Efron revolutionized the field of statistics with his invention of the bootstrap, which he introduced to the world with his paper in the Annals of Statistics. The bootstrap broadly refers to a continually growing collection of methodologies in which data are resampled to incorporate into statistical inference the information contained in the data regarding their probability distribution. Conceptually simple yet computationally intense, the bootstrap owes much of its rise in popularity over the last 20 years to the advent of the personal computer over the same period. As computers become faster and more powerful, the bootstrap becomes a more practical and indispensible tool for the data analyst.

This text, while a complete reference on the topic, is fairly nonmathematical in its treatment of the bootstrap in all its forms. As such, it is accessible not only to statisticians but to persons in all fields interested in inferring conclusions from their data. The book begins with a conceptual discussion of the accuracy of a sample mean and proceeds in the first few chapters to cover a few pertinent basics of probability theory and the properties of the empirical distribution as an estimate of the true cumulative distribution. The distinction between the nonparametric bootstrap and the parametric bootstrap is then discussed, and the impact of the number of bootstrap samples on the estimated standard errors is assessed.

The middle chapters of the text explore bootstrapping different data structures, issues unique to regression models, bootstrap estimates of bias, the jackknife, several forms of bootstrap confidence intervals, permutation tests, hypothesis testing, estimates of prediction error, and using the bootstrap to find an optimal smoothing parameter in nonparametric regression.

The last chapters of the text are more mathematical and serve to provide the theoretical backbone for much of the material presented earlier. Of particular interest to epidemiologists and others in related fields is chapter 25, which covers FDA bioequivalence and shows how bootstrapping can tackle the important issues of power and sample size.

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