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Estimation for the invariant law of an ergodic diffusion process based on high-frequency data

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  • Yoichi Nishiyama

Abstract

Let a one-dimensional ergodic diffusion process X be observed at time points such that and , where , with p∈(0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses.

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  • 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.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:909-915
    DOI: 10.1080/10485252.2011.591397
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    References listed on IDEAS

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    1. Negri, Ilia, 2001. "On efficient estimation of invariant density for ergodic diffusion processes," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 79-85, January.
    2. D. Blanke & B. Pumo, 2003. "Optimal sampling for density estimation in continuous time," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 1-23, January.
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