Efficiency of the empirical distribution for ergodic diffusion
Kutoyants, Yury A.
Bernoulli, Tome 3 (1997) no. 3, p. 445-456 / Harvested from Project Euclid
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We consider the problem of stationary distribution function estimation at a given point by the observations of an ergodic diffusion process on the interval [0,T] as T→∞. First we introduce a lower (minimax) bound on the risk of all estimators and then we prove that the empirical distribution function attains this bound. Hence this estimator is asymptotically efficient in the sense of the given bound.
Publié le : 1997-12-14
Classification:  diffusion process,  minimax bound,  nonparametric estimation 
@article{1175882218,
     author = {Kutoyants, Yury A.},
     title = {Efficiency of the empirical distribution for ergodic diffusion},
     journal = {Bernoulli},
     volume = {3},
     number = {3},
     year = {1997},
     pages = { 445-456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175882218}
}

Kutoyants, Yury A. Efficiency of the empirical distribution for ergodic diffusion. Bernoulli, Tome 3 (1997) no. 3, pp.  445-456. http://gdmltest.u-ga.fr/item/1175882218/