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The Dantzig selector for a linear model of diffusion processes

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  • Kou Fujimori

    (Waseda University)

Abstract

In this paper, a linear model of diffusion processes with unknown drift and diagonal diffusion matrices is discussed. We will consider the estimation problems for unknown parameters based on the discrete time observation in high-dimensional and sparse settings. To estimate drift matrices, the Dantzig selector which was proposed by Candés and Tao in 2007 will be applied. We will prove two types of consistency of the Dantzig selector for the drift matrix; one is the consistency in the sense of $$l_q$$ l q norm for every $$q \in [1,\infty ]$$ q ∈ [ 1 , ∞ ] and another is the variable selection consistency. Moreover, we will construct an asymptotically normal estimator for the drift matrix by using the variable selection consistency of the Dantzig selector.

Suggested Citation

  • Kou Fujimori, 2019. "The Dantzig selector for a linear model of diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 475-498, October.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:3:d:10.1007_s11203-018-9191-y
    DOI: 10.1007/s11203-018-9191-y
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    References listed on IDEAS

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    1. Emmanuel Gobet & Gustaw Matulewicz, 2017. "Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 211-235, July.
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    3. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    4. De Gregorio, Alessandro & Iacus, Stefano M., 2012. "Adaptive Lasso-Type Estimation For Multivariate Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 28(4), pages 838-860, August.
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    6. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
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    Cited by:

    1. Vlad Stefan Barbu & Slim Beltaief & Serguei Pergamenchtchikov, 2022. "Adaptive efficient estimation for generalized semi-Markov big data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 925-955, October.
    2. Kou Fujimori, 2022. "The variable selection by the Dantzig selector for Cox’s proportional hazards model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 515-537, June.

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