Parametric estimation. Finite sample theory

@article{Spokoiny2011ParametricEF,
  title={Parametric estimation. Finite sample theory},
  author={Vladimir G. Spokoiny},
  journal={Annals of Statistics},
  year={2011},
  volume={40},
  pages={2877-2909}
}
  • V. Spokoiny
  • Published 13 November 2011
  • Mathematics
  • Annals of Statistics
The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are: (1) the study is non-asymptotic, that is, the sample size is xed and does not tend to infinity; (2) the parametric assumption is possibly misspecified and the underlying data distribution can lie beyond the given parametric family. The main results include a large deviation bounds for the (quasi) maximum likelihood and the local quadratic… 

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