1979 BootstrapMethods
- (Efron, 1979) ⇒ Bradley Efron. (1979). “Bootstrap Methods: Another Look at the Jackknife.” In: The Annals of Statistics, 7(1). http://www.jstor.org/stable/2958830
Subject Headings: Bootstrapped Resampling, Quenouille — Tukey jackknife; Jackknifing.
Notes
- It is a seminal paper on Bootstrapping.
- It is based on a technical report published on July 5, 1977. http://statistics.stanford.edu/~ckirby/techreports/BIO/BIO%2032.pdf
Cited By
- ~6342 http://scholar.google.com/scholar?q=%22Bootstrap+Methods%3A+Another+Look+at+the+Jackknife%22+1979
Quotes
Abstract
We discuss the following problem: given a random sample [math]\displaystyle{ \mathbf{X} = (X_1, X_2, ..., X_n) }[/math] from an unknown probability distribution [math]\displaystyle{ F }[/math], estimate the sampling distribution of some prespecified random variable [math]\displaystyle{ R(\mathbf{X}, F) }[/math], on the basis of the observed data [math]\displaystyle{ \mathbf{x} }[/math]. (Standard jackknife theory gives an approximate mean and variance in the case [math]\displaystyle{ 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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