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December 1997 Efficiency of the empirical distribution for ergodic diffusion
Yury A. Kutoyants
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Bernoulli 3(4): 445-456 (December 1997).


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.


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Yury A. Kutoyants. "Efficiency of the empirical distribution for ergodic diffusion." Bernoulli 3 (4) 445 - 456, December 1997.


Published: December 1997
First available in Project Euclid: 6 April 2007

zbMATH: 0910.62079
MathSciNet: MR1483698

Keywords: diffusion process , minimax bound , nonparametric estimation

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 4 • December 1997
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