The Dantzig selector for a linear model of diffusion processes

    Research output: Contribution to journalArticle

    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 lq norm for every 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.

    Original languageEnglish
    JournalStatistical Inference for Stochastic Processes
    DOIs
    Publication statusAccepted/In press - 2018 Jan 1

    Fingerprint

    Selector
    Diffusion Process
    Linear Model
    Variable Selection
    Discrete Time Observations
    Unknown Parameters
    High-dimensional
    Estimator
    Norm
    Unknown
    Estimate

    Keywords

    • Dantzig selector
    • Diffusion process
    • High-dimension
    • Sparse estimation
    • Variable selection

    ASJC Scopus subject areas

    • Statistics and Probability

    Cite this

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    title = "The Dantzig selector for a linear model of diffusion processes",
    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 Cand{\'e}s 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 lq norm for every 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.",
    keywords = "Dantzig selector, Diffusion process, High-dimension, Sparse estimation, Variable selection",
    author = "Kou Fujimori",
    year = "2018",
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    doi = "10.1007/s11203-018-9191-y",
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    AB - 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 lq norm for every 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.

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