Threshold Estimation for Stochastic Processes with Small Noise

    研究成果: Article

    抄録

    Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.

    元の言語English
    ページ(範囲)951-988
    ページ数38
    ジャーナルScandinavian Journal of Statistics
    44
    発行部数4
    DOI
    出版物ステータスPublished - 2017 12 1

    Fingerprint

    Least Squares Estimator
    Stochastic Processes
    Filter
    Discrete Observations
    Jump Process
    Asymptotically equivalent
    Justify
    Standard deviation
    Asymptotic distribution
    Stochastic Equations
    Numerical Study
    Shock
    Unstable
    Differential equation
    Estimator
    Unknown
    Threshold estimation
    Stochastic processes
    Least squares estimator

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

    これを引用

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