1979 BootstrapMethods

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Subject Headings: Bootstrapped Resampling, Quenouille — Tukey jackknife; Jackknifing.

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Abstract

We discuss the following problem: given a random sample [math]\mathbf{X} = (X_1, X_2, ..., X_n)[/math] from an unknown probability distribution [math]F[/math], estimate the sampling distribution of some prespecified random variable [math]R(\mathbf{X}, F)[/math], on the basis of the observed data [math]\mathbf{x}[/math]. (Standard jackknife theory gives an approximate mean and variance in the case [math]R(\mathbf{X},F)=\theta(\hat{F})-\theta(F), \theta[/math] some parameter of interest.) A general method, called the “bootstrap," is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.

1. Introduction

The Quenouille — Tukey jackknife is an intriguing non-parametric method for estimating the bias and variance of a statistic of interest, and also for testing the null hypothesis that the distribution of a statistic is centered at some prespecified point. ...


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 abstractAuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
1979 BootstrapMethodsBradley EfronBootstrap Methods: Another Look at the JackknifeThe Annals of Statisticshttp://webber.physik.uni-freiburg.de/~jeti/studenten seminar/stud sem SS 09/EfronBootstrap.pdf1979