DELTA METHOD IN LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR ESTIMATORS

@article{Gao2011DELTAMI,
  title={DELTA METHOD IN LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR ESTIMATORS},
  author={Fuqing Gao and Xingqiu Zhao},
  journal={Annals of Statistics},
  year={2011},
  volume={39},
  pages={1211-1240}
}
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large deviations is proposed. The new method can be widely applied to driving the moderate deviations of… 
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