Bernoulli

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

Efficiency of the empirical distribution for ergodic diffusion

Yury A. Kutoyants

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175882218

Mathematical Reviews number (MathSciNet)
MR1483698

Zentralblatt MATH identifier
0910.62079

Keywords
diffusion process minimax bound nonparametric estimation

Citation

Kutoyants, Yury A. Efficiency of the empirical distribution for ergodic diffusion. Bernoulli 3 (1997), no. 4, 445--456. https://projecteuclid.org/euclid.bj/1175882218


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