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Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

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  • Guy, Romain
  • Larédo, Catherine
  • Vergu, Elisabeta

Abstract

We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ϵσ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ϵ. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ϵ→0 and of (α,β) for Δ→0 and ϵ→0 without any condition linking ϵ and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ϵ based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.

Suggested Citation

  • Guy, Romain & Larédo, Catherine & Vergu, Elisabeta, 2014. "Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 51-80.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:51-80
    DOI: 10.1016/j.spa.2013.07.009
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    Cited by:

    1. Genon-Catalot, Valentine & Larédo, Catherine, 2021. "Probabilistic properties and parametric inference of small variance nonlinear self-stabilizing stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 513-548.
    2. Héctor Araya & Soledad Torres & Ciprian A. Tudor, 2024. "Least squares estimation for the Ornstein–Uhlenbeck process with small Hermite noise," Statistical Papers, Springer, vol. 65(7), pages 4745-4766, September.
    3. Narci, Romain & Delattre, Maud & Larédo, Catherine & Vergu, Elisabeta, 2021. "Inference for partially observed epidemic dynamics guided by Kalman filtering techniques," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    4. Tetsuya Kawai & Masayuki Uchida, 2023. "Adaptive inference for small diffusion processes based on sampled data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(6), pages 643-696, August.
    5. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.

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