Geodesic
Asymptotically efficient importance sampling for the bootstrap
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 82-96

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We establish Large Deviation Principle for conditional moderate deviation probabilities of weighted bootstrap empirical measures given empirical measures. On the base of this result, for the problem of estimation of moderate deviation probabilities of statistics having Hadamard derivatives, we prove asymptotic efficiency of importance sampling based on influence functions. 
@article{ZNSL_2014_431_a5,
     author = {M. S. Ermakov},
     title = {Asymptotically efficient importance sampling for the bootstrap},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--96},
     publisher = {mathdoc},
     volume = {431},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a5/}
}
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M. S. Ermakov. Asymptotically efficient importance sampling for the bootstrap. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 82-96. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a5/