Bootstrap methods and their application.

*(English)*Zbl 0886.62001
Cambridge Series in Statistical and Probabilistic Mathematics, 1. Cambridge: Cambridge University Press. x, 582 p. (1997).

Bootstrap methods are computer-intensive methods of statistical analysis using simulation to obtain reliable standard errors, confidence intervals, and other measures of uncertainty for a wide range of problems. This book gives a broad and up-to-date coverage of bootstrap methods with numerous applied examples, together with the basic theory without emphasis on mathematical vigour. The material of the book is covered in eleven chapters in addition to a bibliography and an appendix.

Chapter 2 describes the properties of resampling methods for use with single samples from parametric and nonparametric models. Chapter 3 extends the basic ideas to several samples, semiparametric and smooth models. Significance and confidence intervals are the subjects of Chapters 4 and 5. The three subsequent chapters deal with resampling methods appropriate for linear regression models, generalized linear models and nonlinear models, and time series, spatial data and point processes. Chapter 9 describes how variance reduction techniques such as balanced simulation can be adapted to yield improved simulations. Chapter 10 describes various semiparametric versions of the likelihood function and the ideas underlying which are closely related to resampling methods. Chapter 11 gives a short introduction to the resampling routines in software packages.

Chapter 2 describes the properties of resampling methods for use with single samples from parametric and nonparametric models. Chapter 3 extends the basic ideas to several samples, semiparametric and smooth models. Significance and confidence intervals are the subjects of Chapters 4 and 5. The three subsequent chapters deal with resampling methods appropriate for linear regression models, generalized linear models and nonlinear models, and time series, spatial data and point processes. Chapter 9 describes how variance reduction techniques such as balanced simulation can be adapted to yield improved simulations. Chapter 10 describes various semiparametric versions of the likelihood function and the ideas underlying which are closely related to resampling methods. Chapter 11 gives a short introduction to the resampling routines in software packages.

Reviewer: K.Alam (Clemson)

##### MSC:

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62G09 | Nonparametric statistical resampling methods |