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Asymptotic Statistics by A.W. van der Vaart

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23

Bootstrap

           This chapter investigates the asymptotic properties of bootstrap estimators for distributions and confidence intervals. The consistency of the bootstrap for the sample mean implies the consistency for many other statistics by the delta method. A similar result is valid with the empirical process.

23.1 Introduction

In most estimation problems it is important to give an indication of the precision of a given estimate. A simple method is to provide an estimate of the bias and variance of the estimator; more accurate is a confidence interval for the parameter. In this chapter we concentrate on bootstrap confidence intervals and, more generally, discuss the bootstrap as a method of estimating the distribution of a given statistic. ...

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