Large deviations for bootstrapped empirical measures

@article{Trashorras2011LargeDF,
  title={Large deviations for bootstrapped empirical measures},
  author={Jos{\'e} Trashorras and Olivier Wintenberger},
  journal={arXiv: Probability},
  year={2011}
}
We investigate the Large Deviations properties of bootstrapped empirical measure with exchangeable weights. Our main result shows in great generality how the resulting rate function combines the LD properties of both the sample weights and the observations. As an application we recover known conditional and unconditional LDPs and obtain some new ones. 

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References

SHOWING 1-10 OF 37 REFERENCES

Exchangeably Weighted Bootstraps of the General Empirical Process

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

Large deviations for subsampling from individual sequences

THE LARGE DEVIATION PRINCIPLE FOR MEASURES WITH RANDOM WEIGHTS

In this paper, we study the problem of large deviations for measures with random weights. We are motivated by previous work dealing with the special case occuring in the statistical mechanics of the

Large and moderate deviations for matching problems and empirical discrepancies

We study the two-sample matching problem and its connections with the Monge-Kantorovich problem of optimal transportation of mass. We exploit this connection to obtain moderate and large deviation

Some Limit Theorems in Statistics

Moment-generating Functions Chernoff's Theorem The Kullback- Leibler Information Number Some Examples of Large Deviation Probabilities Stein's Lemma Asymptotic Effective Variances Exact Slopes of

Large Deviations Techniques and Applications

The LDP for Abstract Empirical Measures and applications-The Finite Dimensional Case and Applications of Empirically Measures LDP are presented.

Large Deviations for Processes with Independent Increments

Abstract : The establishment of the large deviation principle (LDP) has had important implications in various areas in statistics. It has been used to obtain the asymptotic efficiencies of tests and

SOME PROPERTIES OF THE KULLBACK-LEIBLER NUMBER

SUMMARY. In this paper we obtain some useful properties of the Kullback-Leibler (K-L) number. For example, we show that the K-L number is jointly lower semi-continuous in both arguments, on the class

Stein’s method for the bootstrap

This paper gives new proofs for many known results about the convergence in law of the bootstrap distribution to the true distribution of smooth statistics, whether the samples studied come from

Bootstrap relative errors and sub-exponential distributions

For the purposes of this paper, a distribution is sub-exponential if it has finite variance but its moment generating function is infinite on at least one side of the origin. The principal aim here