• Bernoulli
  • Volume 3, Number 4 (1997), 445-456.

Efficiency of the empirical distribution for ergodic diffusion

Yury A. Kutoyants

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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.

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Bernoulli, Volume 3, Number 4 (1997), 445-456.

First available in Project Euclid: 6 April 2007

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diffusion process minimax bound nonparametric estimation


Kutoyants, Yury A. Efficiency of the empirical distribution for ergodic diffusion. Bernoulli 3 (1997), no. 4, 445--456.

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