ABSTRACT
The third chapter introduces the bootstrap method, a general method that can be beneficial in cases where there is no standard procedure to estimate a parameter. The chapter begins with a description of a unified bootstrap framework, including Efron's bootstrap, nonparametric smoothed bootstrap, wild bootstrap, and moon bootstrap. The relationship between bootstrap and Monte Carlo is explained with the help of Efron's sample median example, and the dependency between bootstrap samples is analyzed. The plug-in-principle for basic bootstrap is explained. It is also shown why the bootstrap method is just as good as second-order asymptotic. Different bootstrap methods for calculating confidence sets are presented, including percentile bootstrap, studentized bootstrap (together with the nonparametric delta method), prepivoting confidence regions, and the BC alpha confidence interval.
Further, the bootstrap hypothesis testing, methods for sampling under the null hypothesis, and bootstrap in regression are presented. Finally, the blockwise bootstrapping and stationary bootstrap for time series are included.
The underlying theoretical background of the various methods are explained. All methods are demonstrated with a series of examples and plots. Some of the most important R codes are given. The chapter ends with a list of problems useful for written exams.
