# 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.

## 8 Citations

### A weighted bootstrap procedure for divergence minimization problems

- Economics, Computer Science
- 2015

This work proposes a weighted bootstrap procedure, which produces an explicit procedure which defines the weights, therefore replacing a variational problem in the space of measures by a simple Monte Carlo procedure.

### Minimum Divergence Estimators, Maximum Likelihood and the Generalized Bootstrap

- MathematicsEntropy
- 2021

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit…

### Weighted Sampling, Maximum Likelihood and Minimum Divergence Estimators

- MathematicsGSI
- 2013

This paper explores Maximum Likelihood in parametric models in the context of Sanov type Large Deviation Probabilities in the framework of Sanovo type LargeDeviation Probability models.

### Contributions à la statistique des processus : estimation, prédiction et extrêmes

- Mathematics
- 2012

This habilitation manuscript presents my research work on statistics for weakly dependent processes. Asymptotical results for the Quasi Maximum Likelihood Estimator in general affine models are given…

### Sup-Sums Principles for F-Divergence and a New Definition for t-Entropy

- Computer ScienceJournal of Theoretical Probability
- 2020

A new ‘integral’ definition for t-entropy explicitly establishing its relation to Kullback–Leibler divergence is worked out.

### A Unifying Framework for Some Directed Distances in Statistics

- Computer ScienceArXiv
- 2022

This paper provides a general framework which covers in particular both the abovementioned density-based and distribution-function-based divergence approaches; the dissimilarity of quantiles respectively of other statistical functionals will be included as well.

### Sup-Sums Principles for F-Divergence and a New Definition for t-Entropy

- Computer ScienceJournal of Theoretical Probability
- 2020

New principles for integral F -divergence for arbitrary convex functions F on the whole real axis and arbitrary measures and a new ‘integral’ definition for t -entropy explicitly establishing its relation to Kullback–Leibler divergence are presented.

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