# RESAMPLING FEWER THAN n OBSERVATIONS: GAINS, LOSSES, AND REMEDIES FOR LOSSES

@inproceedings{Bickel2012RESAMPLINGFT, title={RESAMPLING FEWER THAN n OBSERVATIONS: GAINS, LOSSES, AND REMEDIES FOR LOSSES}, author={Peter J. Bickel and Friedrich G{\"o}tze and Willem R. van Zwet}, year={2012} }

We discuss a number of resampling schemes in which m = o(n) observations are resampled. We review nonparametric bootstrap failure and give results old and new on how the m out of n with replacement and without replacement bootstraps work. We extend work of Bickel and Yahav (1988) to show that m out of n bootstraps can be made second order correct, if the usual nonparametric bootstrap is correct and study how these extrapolation techniques work when the nonparametric bootstrap does not.

## 264 Citations

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The Big Data Bootstrap

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The Bag of Little Bootstraps (BLB), a new procedure which incorporates features of both the bootstrap and subsampling to obtain a robust, computationally efficient means of assessing estimator quality, is presented.

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We propose a new method, based on sample splitting, for constructing bootstrap confidence bounds for a parameter appearing in the regular smooth function model. It has been demonstrated in the…

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## References

SHOWING 1-10 OF 76 REFERENCES

The m out of n Bootstrap and Goodness of Fit Tests with Double Censored Data

- Mathematics
- 1996

This paper considers the use of the m out of n bootstrap (Bickel, Gotze, and van Zwet, 1994) in setting critical values for Cramer-von Mises goodness of fit tests with doubly censored data. We show…

Exchangeably Weighted Bootstraps of the General Empirical Process

- Mathematics, Economics
- 1993

We consider an exchangeably weighted bootstrap of the general function-indexed empirical process. We find sufficient conditions on the bootstrap weights for the c~ntral limit theorem to hold for the…

On the Asymptotic Properties of the Jackknife Histogram

- Mathematics
- 1990

We study the asymptotic normality of the jackknife histogram. For one sample mean, it holds if and only if r, the number of observations retained, and d (=n-r), the number of observations deleted,…

When Does Bootstrap Work?: Asymptotic Results and Simulations

- Mathematics, Economics
- 1992

Bootstrap methods are procedures for estimating or approximating the distribution of a statistic based on ideas from resampling and simulation methods. This volume is concerned with the asymptotic…

Second-order properties of an extrapolated bootstrap without replacement under weak assumptions

- Mathematics, Economics
- 1997

This paper shows that a straightforward extrapolation of the bootstrap distribution obtained by resampling without replacement, as considered by Politis and Romano, leads to second-order correct…

When does bootstrap work

- Economics, Mathematics
- 1992

Bootstrap methods are procedures for estimating or approximating the distribution of a statistic based on ideas from resampling and simulation methods. This volume is concerned with the asymptotic…

Richardson Extrapolation and the Bootstrap

- Mathematics
- 1988

Abstract Simulation methods [particularly Efron's (1979) bootstrap] are being applied more and more frequently in statistical inference. Given data (X 1 …, Xn ) distributed according to P, which…

Some properties of incomplete U-statistics

- Mathematics
- 1976

SUMMARY Let g be a symmetric function with k arguments. A U-statistic is the arithmetic mean of g's based on the N = n!/{k! (n- k)!} subsamples of size k taken from a sample of size n. When N is…

Some results on the influence of extremes on the bootstrap

- Mathematics
- 1993

We study the influence of the extremes in the construction of consistent bootstraps in three illustrative situations. These are bootstrapping maxima. bootstrapping intermediate trimmed means and…

Bootstrapping Regression Models

- Mathematics
- 2002

Bootstrapping is a general approach to statistical inference based on building a sampling distribution for a statistic by resampling from the data at hand. The term ‘bootstrapping,’ due to Efron…