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On efficient estimation of invariant density for ergodic diffusion processes

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  • Negri, Ilia

Abstract

The problem of nonparametric invariant density function estimation of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is established. The asymptotic risk considered measures the distance between the estimators and the density that has to be estimate in a functional space endowed with the supremum norm. The local time estimator is asymptotically efficient in the sense of this lower bound.

Suggested Citation

  • Negri, Ilia, 2001. "On efficient estimation of invariant density for ergodic diffusion processes," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 79-85, January.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:1:p:79-85
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    References listed on IDEAS

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    1. Castellana, J. V. & Leadbetter, M. R., 1986. "On smoothed probability density estimation for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 179-193, February.
    2. Yu. Kutoyants, 1998. "Efficient Density Estimation for Ergodic Diffusion Processes," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 131-155, May.
    3. Ilia Negri, 1998. "Stationary Distribution Function Estimation for Ergodic Diffusion Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(1), pages 61-84, January.
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    Cited by:

    1. Yoichi Nishiyama, 2011. "Estimation for the invariant law of an ergodic diffusion process based on high-frequency data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 909-915.

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